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JOSEPH BROWN 






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JOSEPH EE€/WN Icic: 



ELEMENTS 



OF 



LOGIC K; 



OR 



A SUMMARY OF THE GENERAL PRINCIPLES 



AND DIFFERENT MODES 



HF 



REASOIVING. 



BY LEVI HEDGE, L,Ii. D. 

PROFESSOR OF NATURAL RELIGION, MORAL PHILOSOPHY, AND CIVIL POLIXy, 
IN HARVARD UNIVERSITY. 



STEREOTYPE EDITION- 




JSonton: 

PUBLISHED BY IIILLIARD, GRAY & CO. 

ia33. 






DISTRICT OF MASSACHUSETTS, TO WIT: 

District ClerWs Office. 

Be it remembered, That on the fifteenth day of September, A. D. 1827, and in 
the fifty-second year of the Independence of the United States of America, Levi 
Hedge, of the said District, has deposited in this office the title of a book, the right 
whereof he claims as author, in tlie words following, to wit : 

" Elements of Logick; or a Summary of the general Principles and different Modes 
of Reasoning. By Levi Hedge, LL. D. Professor of Natural Religion. Moral Phi- 
losophy, and Civil Polity, in Harvard University." 

In conformity to the act of the Congress of the United States, entitled, ♦* An 
Act for the encouragement of learning, by securing the copies of maps, charts, and 
books, to the authors and proprietors of such copies, during the times therein men- 
tioned :" and also *o an act, entitled, " An Act supplementary to an act, entitled, 
An Act for the encouragement of learning, by securing the copies of maps, charts, 
and books, to the authors and proprietors of such copies, during the times therein 
mentioned ; and extending the benefits thereof to the arts of designing, engraving 
and etching historical and other prints." 

JOHN W. DAVIS, 
Clerk of the District of MassachusetU, 








Stereotyped at the 
Boston Type and Stereotype Faundz-y. 



PREFACE 



TO THE FIRST EDITION, 



Most of the treatises of Logick in common use have 
been formed on the model of the ancient systems, and 
are encumbered with many scholastick subtilties and 
unimportant distinctions. The instructions, which they 
furnish on the subject of ratiocination, consist of very 
little more than a description of the syllogism, and a 
few general principles of demonstrative reasoning. They 
contain no elements nor rules to assist us in reasoning 
on subjects of probability, or on the ordinary events of 
human life. The manner, in which these books are writ- 
ten, is ill adapted to the comprehension of young minds. 
In explaining the operations of reasoning, many technical 
terms and arbitrary forms are employed, of which the 
tendency is rather to embarrass and perplex, than to in- 
struct the learner. 

Though much has been written, of late years, on the 
powers and operations of the mind, yet there have been 
but few attempts to form a system of Logick for the use 
of those, who are commencing the study. Collcrd has 
improved the syllogism, by simplifying its principles, 
and divesting it of its ancient trappings of modes and 
figures. Condillac has proved the importance of the 
method of induction, by pointing out the manner, in 



IV PREFACE. 

which Nature teaches us to analyze the objects, which 
she presents to our observation. In " An Essay on the 
Elements, Principles, and diflferent Modes of Reason- 
ing," by Richard Kirwan, LL. D. all the subjects, which 
properly fall within the precincts of Logick, are amply 
discussed. But this work is too minute and prolix to be 
used as a text book in seminaries of education. Every 
person, who is much conversant with this department of 
knowledge, must have perceived the want of a treatise 
of Logick, more elementary, and better accommodated to 
the present improved state of the philosophy of the mind, 
than any of those, which are now in use. 

The professed object of Logick is to furnish rules for^ 
the direction of the understanding in its various inqui-| 
lies after knowledge. It should, therefore, teach the 
principles of every species of reasoning, which we have] 
occasion to make use of, both in the pursuits of science, 
and in the ordinary transactions of life. Demonstrative! 
reasoning can be employed only about general truths, 
and such relations as are in their nature immutable. 
It is of little use in regulating our judgments and con- 
clusions concerning events, which are irregular in theirl 
occurrence, and which depend on contingent circum-| 
stances. To reason on subjects of this kind, it is neces- 
sary to understand the nature of moral evidence, andl 
the grounds of probability. It is by moral evidence 
alone, that we reason on historical facts, and the casual| 
occurrences of life. It is also this evidence, which influ- 
ences our conclusions on the important and interesting] 
subjects of government, morals, and religion* 



PREFACE. V 

Under these impressions, the writer of this compend 
as pursued the following plan. After passing through 
he customary distinctions of terms and propositions, he 
las given a brief account of moral evidence, and pointed 
ut the circumstances, which distinguish it from demon- 
trative. A concise view is then given of the different 
)rms of reasoning, with the principles, on which they 
spectively proceed. 

The books, which have been principally consulted in 
)rming this summary, and in which the greatest part 
f the following principles may be found, are Watts' 
-ogick, Locke's Essay on the Understanding, Reid's 
!ssays on the Intellectual Powers, Stewart's Elements 
* the Philosophy of the Mind, Beattie's Essay on Truth, 
atham's Chart and Scale of Truth, Collard's Essentials 

Logick, Kirwan's Logick, Campbell's Philosophy of 
hetorick. Gambler's Introduction to Moral Evidence, 
elsham's Compendium of Logick, and Scott's Elements 
■ Intellectual Philosophy. 

Where passages have been borrowed entire, credit is 
ven in the usual way. At the close of the several 
lapters may be found the names of those authors, from 
hom particular assistance has been derived. 
1* 



PREFACE 



TO THE THIRD EDITION. 



The present edition of the Elements of 
Logick is printed in a smaller type than either 
of the preceding, in order that the copies 
may be afforded at a reduced price. The 
author has carefully revised the work, and 
has enlarged it by the addition of a few pages, 
containing some general principles and rules 
respecting controversy, and also a system of 
rules for the interpretation of written docu- 
ments. These have been collected with care 
from authors of high reputation, and, it is 
hoped, will not be thought an unsuitable 
appendage to a system of logick. In a few 
places, slight alterations have been made in 
the language and in the arrangement ; and 
some notes have been inserted at the end of 
the book, which were not in the preceding 
editions. 

JIarvard College, Nov, 1821. ^ 



CONTENTS. 



PART FIRST. 

A DESCRIPTION OP THE LEADING AFFECTIONS AND 
OPERATIONS OF THE MIND. 

P&go 

Introduction • • 13 

CHAP. I. 
Perception and Consciousness 15 

CHAP. II. 
Attention. 19 

CHAP. III. 
Comparing • • • • • 21 

CHAP. IV. 
Abstraction. 23 

CHAP. V. 
Association 25 

CHAP. VI. 
Analysis. • ....••. 28 



PART SECOND. 

OF TERMS AND PROPOSITIONS. 

CHAP. I. 
Logical Distinctions of Terms 31 



X CONTENTS. 

CHAP. II. 
Definition and Division .39 

CHAP. III. 
General Description of Propositions 43 

CHAP. IV. 

Simple, Complex, and Modal Propositions. . . .47 

CHAP. V. 

Quality and Quantity of Propositions .'60 

CHAP. VI. 
Opposition and Conversion of Propositions. ... 55 

CHAP. VII. 
Compound Propositions 59 

PART THIRD. 

OP JUDGMENT AND REASONING. 
CHAP. I. 

Intuitive Evidence. . 65 

CHAP. II. 

Difference between Moral and Demonstrative 

Reasoning 70 

CHAP. III. 
Induction 76 

CHAP. IV. 
Analogy 83 

CHAP. V. 

Reasoning on Facts • 88 



CONTENTS. XI 

CHAP, VI. 
Calculation of Chances 101 

CHAP. VII. 

General Description of Demonstrative Reasoning. 108 

CHAP. VIII. 
Distinctions of Reasoning. . 113 

CHAP. IX. 

General Description of Syllogistick Reasoning. . 116 

CHAP. X. 
Regular Syllogisms .120 

CHAP. XI. 
Bnthymemes. .130 

CHAP. XII. 
Conditional and Disjunctive Syllogisms 134 

CHAP. XIII. 
Compound Syllogisms • • • I^*' 

CHAP. XIV. 
Sophisms. • • 144 

CHAP. XV. 
Disposition or Method 149 

CHAP. XVI. 
Rules of Controversy. • • • • 157 

CHAP. XVII. 
Rules of Interpretation. 162 

Concluding Remarks • • • • • 168 

Notes and Illustrations, •••••••• 171 



ELEMENTS OF LOGICK. 



PART FIRST. 

A DESCRIPTION OF THE LEADING AFFECTIONS AND OPERA- 
TIONS OF THE MIND. 



INTRODUCTION. 

1. The purpose of Logick is to direct the 
intellectual powers in the investigation of truths 
and in the communication of it to others. Its 
foundation is laid in the philosophy of the hu- 
man mind, inasmuch as it explains many of 
its powers and operations, and traces the pro- 
gress of knowledge, from the first and most 
simple perceptions of outward objects, to those 
remoter truths and discoveries, which result 
from the operations of reasoning. 

2. Logick instructs us in the right use of 
terms, and distinguishes their various kinds. 
It teaches the nature and varieties of propo- 
sitions ; explains their properties, modifica- 



14 



INTRODUCTION. 



tions, and essential parts. It analyzes the 
structure of arguments, and shows how their 
truth may be discovered, or their fallacy de- 
tected. Lastly, it describes those methods of 
classification and arrangement, which will best 
enable us to retain and apply the knowledge, 
which we have acquired. 

3. Though the understanding would be in- 
capable of any high degree of improvement, 
without the aid of rules and principles, yet 
these are insufficient without practice and ex- 
perience. The powers of the mind, like those 
of the body, must be strengthened by use. 
The art of reasoning skilfully can be acquired 
only by a long and careful exercise of the 
reasoning faculty, on different subjects and in 
various ways. The rules of logick afford 
assistance to this faculty, not less important 
than that, which our animal strength derives 
from the aid of mechanical powers and en- 
gines. They guide its operations, and supply 
it with suitable instruments for overcoming the 
difficulties, by which it would be impeded in 
its search after truth. 

4. In the following compend, the subjects 
of logick are distributed into three parts. The 



PERCEPTION AND CONSCIOUSNESS. 13 

first contains a brief description of the lead- 
ing powers and operations of the mind : The 
second, of the several kinds of terms and prop- 
ositions. The third comprises an explanation 
of moral and demonstrative evidence ; of the 
difTeient modes of reasoning ; of sophisms ; 
and of method, or disposition. 



CHAPTER FIRST. 

PERCEPTION AND CONSCIOUSNESS. 

5. Perception is the first state or aflfection 
of the human mind. By this we gain all our 
knowledge of the powers and qualities of the 
material objects about us. The instruments 
of perception are the five corporeal senses, 
seeing, feeling, hearing, tasting, and smelling. 
All the intercourse, which the mind has with 
the material world, is carried on by these 
organs. Of the manner, in which this in- 
Itercourse proceeds, we have no knowledge. 
From experience w^e learn, that a sensible 
alteration takes place in the mind, whenever 
|any outward object is so situated, as to aflfect 
lither of the senses. The change^ produced 
in the mind by the impression of the object on 
Ithe organ of sense, is denominated sensation. 



16 PERCEPTION AND CONSCIOUSNESS. 

The word perception denotes the hioivledgCj 
that we gain by sensation, of some quality iA the 
object ;^ which knowledge may be retained by 
the mind after the object is removed, and it 
is then usually called an idea ox notion. The 
external object, or quality perceived, is de- 
nominated the object of perception] or the 
archetype of the idea. 

6. If either of the senses be wholly wanting, 
the mind must be forever destitute of all that 
class of ideas, which it is the office of that 
sense to furnish. If either be po^essed but 
imperfectly, the ideas, received from it, arc 
liable to be faint and indistinct. But the usual 
effects of dull organs may be in a great measure 
obviated, by an increased effort of attention, 
while the objects are present ; as is manifest 
in the case of persons, who have had their 
hearing in some degree impaired. 

It is from habitual inattention to our sensa- 
tions, more than from dulness in the organs 

* " The sensations J which are excited in the mind by external 
*' objects, and the perceptions of material quahties, which follow 
'^ those sensations, are to be distinguished from each other only 
" by long habits of patient reflection/' Sieicart, Elem. vol, i. ch. v 
part 2d; sect. 1st 



PERCEPTION AND CONSCIOUSNESS. 17 

of sense, that so few of the objects, which 
strike our senses, leave any durable traces in 
the mind ; and that those notions, which do 
remain, are so often obscure and indistinct. 
As the perceptions of sense are the first ele- 
ments of our knowledge, we should cultivate 
the habit of carefully noticing the things, which 
we see, feel, and the like ; in order that the 
notions, which we form of them, may be clear 
and distinct. 

7. Consciousness^ or reflection^ is that 7iotice, 
tvhich the inind takes of its own operations^ 
and modes of existence."^ By this we are 
made acquainted with the successive changes^ 
which take place in the state of our minds. 
Consciousness is similar to perception, though 
the qualities of body, which are the objects of 
the latter, bear no resemblance to the thoughts 
and operations of the mind, which are the 
objects of the former. The mind, at least 
whilst we are awake, is constantly employed 
in some mode of thinking, or in some exertion 
of its powers ; and all the operations, passions, 
and affections of the mind, are necessarily 
ubject to its own observation. Thus, by 

* See note A, at the end of the book. 

2* 



18 PERCEPTION AND CONSCIOUSNESS* 

consciousness, we learn what is expressed by 
the words compare^ reason^ doubts assent, joy, 
in the same manner as, by perception, we gain 
a knowledge o{ siueet, green, soft, cold. 

8. Both perception and consciousness, consid- 
ered apart from any acts of attention, accom- 
panying them, are involuntary states of mind. 
We are often active in bringing external objects 
within our view, and in varying their position, 
for the purpose of careful observation ; so, by 
a voluntary effort, we excite operations, and 
cause changes in the mind ; but the knowl- 
edge, that we gain in each case, of the subjects| 
thus presented, is without any act of the will. 
We cannot avoic hearing many sounds, and 
seeing the objects, which are placed before our 
eyes. We are constrained to smell odours, 
taste our food, and feel bodies, when in contact 
with our own. It is the same with respect 
to the operations and states of the mind. We 
are unable to compare, reason, abstract; to| 
feel pain, pleasure, disgust, or the hke, without 
being conscious of those states. 



ATTENTION. 19 

CHAPTER SECOND. 

ATTENTION. 

9. Attention expresses the immediate direc- 
tion of the mind to a subject. The distinctness 
of our notions, the correctness of our judg- 
ments, and the improvement of all our intel- 
lectual powers, depend-, in a great degree, on 
the habitual exercise of this act. Its surprising 
influence, in improving the perceptive powers, 
is manifest in persons, who have been led, by 
their peculiar callings, or by necessity, to place 
uncommon reliance on a particular sense. 

Thus sailors, who are accustomed to look 
at distant objects, acquire the power of seeing 
and distinguishing things, which, by reason of 
their distance, are invisible to common eyes.^ 
Musicians become capable of discerning the 
minutest difference in sounds. Cooks and 
epicures acquire an uncommon sensibility in 
tasting and smelling ; and blind persons im- 
prove the sense of feeling to such a degree, as 
to make it, in some measure, supply the want 
of sight. These effects are produced chiefly 
by an increased and habitual attention, which 

* A seafaring life, especially when early commenced, has a ten- 
dency to produce some physical change in the organ of vision. 



20 



ATTENTION 



enables those persons to notice impressions, 
which are so sHght and languid, as wholly to 
escape the observation of others. 

10. Attention is considered^ a voluntary act 
of the mind, but it is not at all times equally 
subject to our command, and in young children 
is wholly involuntary. Extraordinary occur- 
rences, which awaken curiosity, and things, 
w^hich interest us in a high degree, by exciting 
some violent passion or emotion, often draw 
the attention so strongly, that we are unable 
for a time to transfer it to any other subject. 
So intensely are we sometimes engaged, that 
we lose our account of time, and take no notice 
of the objects, which strike the senses. 

11. Attention is so essential to memory, that, 
without some degree of it, no thought could 
ever be recalled ; and the reason why we com- 
mit things to memory more easily at one time, 
than another, is, that we command our atten- 
tion more perfectly. It is equally necessary 
in every operation of comparing, judging, and 
reasoning. Dr. Reid has remarked, " that, if 
'' there be any thing that can be called genius, 

* Stewart, Elements of the Philosophy of the Mind, vol. i. ch. 2 
Reid, Essays on the Active Powers, Essay II. ch. 3. 



COMPARING. 21 

" in matters of mere judgment and reasoning, 
" it seems to consist chiefly in being able to 
'' give that attention to the subject, which keeps 
" it steady in the mind, till we can survey it 
" accurately on all sides. There is a talent 
*' of imagination, which bounds from earth to 
" heaven, and from heaven to earth, in a mo 
'• ment. This may be favourable to wit and 
" imagery ; but the powers of judging and rea- 
" soning depend chiefly on keeping the mind 
'• to a clear and steady view of the subject."* 



CHAPTER THIRD. 

COMPAEING. 

12. When the mind contemplates two things 
in reference to each other, it performs the 
operation of comparing. Thus, when we say 
iron is harder than lead, and lead is heavier 
than iron, we compare these two substances 
with respect to the degrees, in which they 
possess the qualities of weight and hardness. 
From this operation we derive all our notions 
of relation ; as father, cousin^ largeness, small- 
ness, superiority, subjection, and the like. 

* Essays oh the Active Powers, Essay II. ch. 3. 



22 COMPARING. 

We make comparisons with the greatest ease, 
and frequently without being conscious of them. 
It is only by this operation, that we are enabled 
to recognise the objects, v/hich we have before 
known, or to give to any quality or object an 
appropriate name ; for the application of the 
name requires not only the sensation, produced 
by a present object, but the comparison of that 
sensation with one formerly felt.^ 

13. This operation is performed by children 
in their earliest efforts at speech. It is by 
successively comparing the sounds, they utter, 
with those, made by others, that they learn to 
pronounce the words of their native tongue. 
That propensity to imitation, which is always 
conspicuous in the sports of children, is hap- 
pily calculated to improve this effort of the 
mind. The same may be asserted of many of 
those studies, which usually occupy the years 
of childhood, and particularly of the study 
of foreign languages. Translations from one 
language into another require a constant and 
careful comparison of the corresponding words 
of different languages ; an exercise doubly 

* Stewart, Elements, vol. i. ch. 3. 



ABSTRACTION. 23 

iraportant to children, as it serves to improve 
their discerning faculties, and at the same time 
leads them to ascertain the exact import of 
words. The correctness of every process of 
judgment and reasoning depends, immediately 
or ultimately, on the accuracy of our compari- 
sons. 



CHAPTER FOURTH. 

ABSTRACTION. 

14. Abstraction literally implies the separa- 
ting of one thing from another ; but, as a 
mental operation, it denotes only a partial 
consideration of any thing. It is the act of 
considering one or more of the properties or 
circumstances of an object^ apart from the rest. 
Thus we may consider the length of a bridge, 
ithout regarding its breadth or construction, 
e may speak of fluidity in water, hardness in 
arble, or sweetness in sugar, without noticing 
he other properties of those substances. As 
he quality, thus mentally separated from those 
xisting Avith it, may be found in numerous 
ubjects, the name applied to it becomes a 
eneral term. So whiteness stands for the 



24 



ABSTRACTION. 



colour of snow, milk, chalk, paper, and many 
other things. 

15. This power, which the mind has, of 
separating the qualities combined in the ob- 
jects, which fall under our observation, and of 
tracing the same quality in a multitude of ob- 
jects, is the foundation of all classification, 
and gives rise to the general words of language 
But, notwithstanding the necessity of abstrac- 
tion in every act of classification, it may be 
performed on individuals, without referring 
them to any class. This has occasioned some^ 
to suppose, that the formation of classes re- 
quired a distinct operation, which they called 
generalization. Dr. Reid says, "we cannot 
"generalize without some degree of abstrac- 
" tion, but I apprehend we may abstract without 
" generalizing. For what hinders me from at- 
" tending to the whiteness of the paper before 
" me, without applying that colour to any other 
" object ? The whiteness of this individual 
" object is an abstract conception ; but not a 
" general one, while applied to one individuai 
"only. These two operations, however, are 

* Reid, Intellectual Powers, Essay V ch. 3. Collard, Logick, 
part I. ch. 2. 



ASSOCIATION 25 

'^subservient to each other; for the more at- 
" tributes we observe and distinguish in any 
'^ one individual, the more agreements we shall 
'' discover between it and other individuals/' 



CHAPTER FIFTH, 

ASSOCIATION, 

16. By the associatioii of ideas is understood 
that connexion among the thoughts^ affections^ 
and operations of the mind^ by ivhich one has 
a tendency to introduce another. That one 
idea is often suggested to the mind by another, 
and that sensible objects revive past trains of 
thought, are facts familiar to all. Words re- 
call the objects, to which they have been ap- 
plied ; and the objects as readily suggest their 
names. A long train of associated thoughts 
is sometimes introduced by a single circum- 
stance. The view of the spot, where we passed 
the first years of life, after a long absence, will 
recall many interesting events of childhood. 
The first notes of a familiar tune, being sound- 
ed, will cause the remaining notes to pass 
through the mind in regular order. 

17. No principle of our nature is productive 
lof more important effects, than this, which 



26 



ASSOCIATION. 



establishes a connexion between our ideas, 
feelings, and mental operations. It is the source! 
of numerous errors and prejudices. It is the 
foundation of all our local attachments ; and of 
most of our prepossessions in behalf of the gov- 
ernment and other institutions of our country. 
It is to the principle of association, that we are 
to attribute our predilections for the modes of 
dress, pronunciation, and behaviour of those, 
whom we esteem and respect. 

The principles of association have been dif- 
ferently stated. Their number is not settled ; 
but the following are among the most obvious : 

18. First, resemblance or analogy is an ex- 
tensive principle of association. We are often 
reminded of one person, by the countenance, 
voice, or gestures of another. One natural 
scene suggests another ; and one event or one 
anecdote frequently brings another to our re- 
membrance, by the similarity we observe be- 
tween them. 

19. Secondly, opposition or contrast is another 
principle of association, but of less extensive 
influence than the preceding. The pains of 
hunger and thirst suggest the pleasures of 
eating and drinking. Cold reminds us of 



ASSOCIATION. 27 

neat ; darkness, of light ; and parsimony, of 
prodigality. So, among contending parties, 
extravagance on one side usually drives the 
other to the opposite extreme. 

20. Thirdly, another, and with the bulk of 
mankind the most extensive, ground of as- 
sociation, is contiguity or nearness of time and 
place. The recollection of an event, in which 
we were interested, brings to our thoughts 
many circumstances connected with it ; as the 
place we were in, when it happened, or when 
we were informed of it ; the persons, who were 
with us ; and the peculiar state of our feelings 
at the time. The objects we meet on a road, 
that we have formerly travelled, successively 
remind us of the subjects, about which we were 
employed, when we passed them before. 

21. A fourth principle of association re- 
sults from the relations of cause and effect^ 
premises and consequences. The sight of a 
surgical instrument, or an engine of torture, 
excites a strong sense of the pain, it is calcu- 
lated to occasion ; and the sight of a wound 
reminds us of the instrument, by which it was 
made. When we see a fellow being in distress, 
we are solicitous to find out the cause ; and 



28 ANALYSIS. 

when we have afflictive tidings to communicate, 
we anticipate the grief, which will be excited. 
22. As one idea may be associated with se- 
veral othersj each leading to a different series. 
it is obvious, that the same circumstance may] 
suggest different trains of thought to differem 
persons, and to the same person at different 
times. The association of ideas is concernedl 
in every act of memory and recollection. Ni 
thought, after it has once passed from the! 
mind, could ever be recalled, were it not for 
the tendency of one idea to introduce another •*! 



CHAPTER SIXTH. 

ANALYSIS. 

23. Analysis deserves a place among thej 
operations, by which the elements of knowledge 
are acquired. Without this, our perceptive 
powers would give us. only confused and im- 
perfect notions of the objects around us. To 
analyze is nothing more^ than to distinguish 
successively the several parts of any compound 
subject. Nature dictates this process. We 

* Hume, Essays, vol. ii. sect. 3. Stewart, Elem. vol. i. ch. 5. 
Beattie, Dissertations, Mor. and Grit. vol. i. ch. 2, sect. i. Scott, 
Elem. Intel. Phil. ch. v. sect. i. 



ANALYSIS. 29 

commence it at the earliest period of improve- 
ment, and practise it in all our efforts to obtain 
in formation. The objects, which nature pre- 
sents to us, consist of assemblages of different 
qualities, some more and others less easily dis- 
iiruaiished. Children early become acquainted 
with the distinguishing properties of the things, 
daily offered to their senses, and in a few 
years find out the characteristiok marks of 
numerous classes of things, and learn the use 
of language. 

24. Things, which have no immediate re- 
ference to material objects, such as thoughts, 
affections, and mental operations, are analyzed 
in the same manner as objects of sense. The 
words abstract and reasoji denote processes of 
thought, each of which may be readily distin- 
guished into separate parts, and these parts 
into others more remote. The same may be 
said of moral qualities, as justice, prudence, 
benevolence, and the like. In these, as in 
sensible objects, there are certain parts, which 
are instantly noticed, and others, which are 
discovered by attentive observation. The 
analysis begins in both cases with the leading 
3* 



30 ANALYSIS. 

qualities, and becomes more perfect as new 
qualities are discovered. 

25. We employ analysis in interpreting 
symbolical language and ambiguous proposi- 
tions. Analysis enables us to investigate causes 
by their effects, and to find out the means 
necessary to attain an end proposed, by having 
the end first in view. It is by this instrument, 
that the chymist and botanist retrace the pro- 
cesses of nature, and ascertain the qualities of 
mineral and vegetable substances. 

Analysis will be further considered under 
the head of Inductive Reasoning.* 

* Condiliac, Logick, part i. Watts, Logick, part iv. ch. 1. Stew- 
art, Elem. vol. ii. ch. 4. 



PART SECOND- 

OF TERMS AND PROPOSITIONS, 



CHAPTER FIRST. 

LOGICAL DISTINCTiONS OF TERMS. 

26. Words possess no natural aptness to 
denote the particular things, to which they are 
applied, rather than others, but acquire this 
aptness wholly by convention. Had the con- 
nexion between the name and the thing been 
established by nature, there would have been 
but one language in the world. But we find 
different words employed in different countries, 
and with equal advantage, to signify the same 
thing. Thus white^ alhus^ and hlanc^ denote 
the same colour. The principal distinctions 
of terms in logick are the following : 

27. First, terms are either simple or com- 
plex. A simple term is a single word ; as man, 
horse, tree. A complex term consists of tivo 
or more words, representing some object or asso- 
ciation, formed to be the subject or predicate 
of a proposition ;^ as, human fortitude, a swift 

* See ch. 3. 



32 TERMS. 

horse, an amiable deportment. A word^ ivhich 
denotes several individuals of the same sail^ is\ 
called a collective term ; as, army, forest, drove. 

28. Secondly, terms are distinguished into 
absolute and relative. An absolute terin is one^ 
ivhich represents an object or quality^ ivithout 
intimating its relation to any other thing ; as, 
man, river, mountain, roundness, strength. A 
relative term denotes an object so far only as 
it is connected ivith some other object. Thus, 
father implies a man primarily, as he is con- 
sidered the cause of existence to another in- 
dividual, denominated, in reference to him, 
son. These two terms, intimating each other, 
by a reciprocal reference, are called correlative. 
So patron and client^ husband and wife, guardian 
and ivardj are correlative terms. 

There are other relative terms, as who, 
which, it, that, and the like, which barely 
recall certain other w^ords, before mentioned ; 
hence the words they refer to are denominated 
antecedents. 

29. Thirdly, terms are distinguished into 
univocal, equivocal, and synonymous. Univocal 
terms are such as have invariably the same 
signification annexed to them. Thus individual- 



TERMS. S3 

%? ^enw5, electricity^ are univocal terms ; 
for they always signify the same things. 
Equivocal words are such as are employed in 
different senses. Of this sort is the word headj 
which may signify a part of a nail, of an 
animal, or of a discourse. So the words post 
and shore are equivocal*; for they are used in 
various senses. 

That some words should be used in different 
senses is unavoidable, on account of the scanti- 
ness of language, which does not afford a 
distinct name for every idea. Notwithstanding 
this, we sometimes find two or more words 
applied to the same thing : as ivave and billoiv^ 
dwelling and habitation. These are called 
synonymous terms. 

30. A fourth distinction of terms is into 
abstract and concrete. An abstract term is one^ 
which signifies some quality or attribute^ ivithout 
referring to any subject^ in ivhich it may be 
found; as roundness, hardness, equality, firm- 
ness. Concrete terms denote both the attributes 
and the subjects^ to which they belong. Some- 
times they express the subjects directly^ and 
the attributes indirectly ; and sometimes the 
reverse Thus philosopher^ statesman^ me- 



34 



TERMS. 



chanick^ are concrete terms, which directly 
denote persons, and indirectly the attributes, 
for which they are distinguished. But ivise^ 
valiant^ swift^ hard, are concretes, immediately 
signifying certain attributes, and indirectly 
intimating the persons or things, to which 
they belong. 

31. Fifthly, terms are either singular or 
universal. A singular term is the proper name 
of some individual person, place, or thing ; as 
Alexander, London, Danube, Etna. Proper 
names are given only to those things, which 
we have frequent occasion to mention, as 
individuals. The design of proper names is 
to represent these, apart from the classes, to 
which they belong. Any term, that does this 
office, is a proper name ; and loses not its 
character as such by being applied, as it fre- 
quently is, to several individuals of the same 
kind, as Peter, John, William. 

32. Universal terms, otherwise denominated 
common or appellative, are names indiscrimi- 
7iately applicable to many individual beings^ 
whether natural or artificial, by reason of 
certain properties, which they possess in com- 



TERMS. 35 

mon Thus man, city^ river^ mountain^ are 
universal terms, because they agree to all men, 
cities, rivers, and mountains. 

33. Universal terms make the greatest part 
of the v^ords of every language. Their sig- 
nification is designedly imperfect ; comprising 
only the most common and obvious properties 
of things. They are abridgments of language, 
happily contrived to facilitate and expedite 
the intercourse of society. Every production 
of nature and art, and every property of mind 
and body, is an individual. Each has some 
properties peculiar to itself ; and others, which 
it possesses in common with many other beings. 
By discarding the peculiar properties, and re- 
taining under distinct names those, which are 
common, we reduce to a limited number of 
classes the innumerable objects, which fall 
under our observation. This distribution of 
things into classes forms what logicians call 
the genera and species of things. 

34, Species denotes a sort or class^ including 
only i7idividuals , and genus a class including 
under it tico or more species. A species is 
formed by applying a name to that property, 
or collection of properties, in which many 



36 TERMS. 

individuals are found to agree. Thus man is a 
species ; for the name is appHcable to an in- 
definite number of individual beings, on account 
of their agreeing in the essential properties 
of an erect figure, and the faculties of speech 
and reason. So horse^ deer^ eagle^ tree^ 
are species. Genus implies the property or 
properties, vv^hich different species possess in 
common. Thus the property of walking on 
four feet is the foundation of the genus quad- 
ruped^ v^hich applies to horse^ lion^ dog^ 
elephant^ and many other species. So bird 
is a genus, of which eagle^ lark, sivan^ and 
sparrow^ are species. 

35. In the distribution of things into genera 
and species, regard is had to the comprehension 
and extension of general terms. By the com- 
prehension of a term is meant the aggregate of 
all the knoivn properties of that things or class 
of things^ to which it is applied. Thus gold 
includes in its comprehension a material sub- 
stance, a yellow colour, superior weight, 
ductility, fusibility, and every other known 
property of that body. The extension oj a term 
regards the number of individual subjects^ to 
which it may be applied. So the term gold 



TERMS. 37 

includes in its extension every separate parcel 
of that metal. Man includes in its extension 
every individual of the human race. 

SQ. Classes are multiplied as the conveni- 
ence of language is found to require ; nature 
having affixed no limits to the number, that 
may be formed. As the number of classes 
increases, the names, which express them, 
become more complicate in their signification, 
and less extensive in their application to indi- 
viduals. Hence it is received as a maxim in 
logick, that, c^'the compreheuhion of a general 
term is enlarged^ its extensio7i must he dimin- 
ished ; and the contrary. The comprehension 
of any species is ^obviously greater than that 
of the genus, to which it is subordinate ; for 
the species includes all the attributes of the 
genus, and others in addition. Thus, in the 
following subordinate -'terms, sj^alloivl birdj 
animalj all the attributes of bird are found in 
swallow^ and all those* of amma/, in bird ; but, 
in each remove, a part of the first collection of 
attributes is discarded. The case is different 
with respect to their extension ; that of animal 
is much greater than that of bird^ and that of 
bird greater than that of swallow. 
4 



38 TERMS. 

37. The ranks, which He above any class, 
or which embrace a wider extension, are 
called, in reference to it, superior ; and that, 
which terminates the series, is called most ^e- 
neral^ or the highest genus. Descending from 
this, each rank is called inferior ; and the low- 
est class, which includes only individuals, is 
called the lowest species. All the intermediate 
ranks, between the highest genus and the 
lowest species, are termed subaltern ; each 
being indifferently either a genus or a species, 
according as it is considered in the ascending 
or descending series. Thus bird is a genus, 
when referred to eagle^ raven^ sparrow^ but 
a species, when referred to the more general 
term, animal. 

38. The genus next above any species is call- 
ed the proximate genus, and any genus above 
that, a remote genus of tRat species. Thus 
quadruped is the proximate, and animal a re- 
mote genus of horse. The property, or collection 
of properties, by which any species is distin- 
guished from every other species of the same 
genus, is the specif ck difference. So juice 
is the proximate genus of ivine ; but the cir- 
cumstance of being pressed /rom grapes is the 



DEFINITION. 39 

specifick difference, which distinguishes wine 
from cider and perry, which are also juices.^ 



CHAPTER SECOND. 

DEFINITION AND DIVISION, 

39. Definitions are usually distinguished into 
two kinds : one nominal^ or of the name ; 
the other real^ or of the thing. A definition 
of the name is merely a specification of the 
object^ to which a name is applied. A definition 
of the thing is properly an analysis of a thing, 
or an enumeration of its principal attributes. 

40. Words, which stand for indivisible ob- 
jects, admit only of nominal definitions. These 
are sometimes sufficiently explained by intelli- 
gible synonymous words ; thus being denotes 
existence ; identity implies sameness. Those, 
which stand for simple qualities of body, may 
be defined by referring to the subjects, in which 
those qualities reside ; and those, that denote 
mental states, by describing the occasions, on 
which they are produced. Thus yellow is the 

* Locke, Essay on the Understanding, b. iii. ch. 3. Reid, Essays, 
vol. ii. essay v, ch. 1. Belsham, Logick, part i. sect. 4 and 5. 
Kirwan, Logick, part i. cb. 2, sect. 2. 



40 DEFINITION. 

colour of gold or saffron. Surprise is the 
passion^ or state of mind, produced by the 
perception of some new or uncommon object. 

41 . A real definition leads us to a knowledge 
of the nature of a thmg, by enumerating its 
most essential modes and properties. Thus a 
circle is a figure, whose circumference is, in 
every part, equally distant from the centre. 
Injustice is an intentional violation of another^s 
rights. Real definition includes the nominal ; 
for an explanation of the nature of any thing 
necessarily fixes the signification of the name, 
by which it is called. Natural substances, and 
all compound beings, whether real or imaginary, 
are susceptible of real definitions. 

42. Logicians divide a definition into two 
parts, which are called genus and difference. 
If the thing to be defined be in any degree 
general, that is, expressed by a generick term, 
the definition will be made up of the proxi- 
mate genus and the specifick difference. Thus 
bird is an animal, which has wings, feathers, 
and a hard, glossy bill. Animal is the proxi- 
mate genus, denoting what bird has in com- 
mon with horse^ deer, elephant ; the other 
terms denote the specifick difference ; for they 



DEFINITION. 41 

point out the properties, which distinguish 
bird from every other species of animals. So 
square is a figure, which has four equal sides, 
and four right angles. Figure is the proximate 
genus ; the other terms make the specifick 
difference. 

43. If the thing to be defined be an individ- 
ual, having a proper name, the definition will 
consist of the species and an enumeration of 
so many properties, as will distinguish that in- 
dividual from all others of that species. Thus 
Mercury is the planet nearest the sun. Planet 
is the lowest species ; nearest the sun is 
the circumstance, which sufficiently marks a 
difference between Mercury and the other 
planets. 

44. There are many words in every lan- 
guage, which cannot be defined, because they 
have no uniform signification affixed to them. 
The^ thisy that, which, such, every, good, had^ 
desirable, and the like, are nearly insignificant 
sounds, till they are applied to particular 
things, from which they borrow a sort of local 
or temporary meaning : and they often signify 
different things, when applied to different 
subjects. Good, applied to a soldier, means 

4^ 



42 DEFINITIOi?r. 

courage ; to a Christian, piety ; to a physician, 
skill ; to a horse, strength ; to a knife, sharpness. 

45. Words of this description, which have 
no uniform signification affixed to them, are 
wholly employed in the definition of other 
terms. The definitive particles have no other 
use, than to restrain the latitude of general 
terms. For example, the man, this horse, that 
tree, such an object. Here the names man^ 
horse, tree, and object, w^hich represent whole 
classes of things, are restrained, by the words 
the, this, that, and such, to certain individuals, 
wdth which we are supposed to be already 
acquainted. 

Again, a wide river, a severe winter, a de- 
lightful prospect. The terms river, lointer, 
and prospect, are general ; wide, severe, and 
delightful, denote specifick diflferences. Where- 
ever the latitude of a general word is restrained 
by a definitive, or a quality is attributed to 
a subject, we may recognise the two essential 
parts of a definition, namely, genus and diflfer- 
ence. 

46. Division is the explication of any ivhole 
by the enumeration of its component parts. 
Thus a tree is divided into trunk, roots, and 



PROPOSITIONS* 43 

branches ; animal^ into beast, bird, fish, and 
insect. The term, division^ is applicable to 
the resolution of a treatise or discourse into 
its several heads or branches ; also, to the 
consideration of an equivocal word in reference 
to its different significations. 

The members of a division should exhaust 
the subject divided ; and they should be so 
opposed, that one will not be contained in 
another. The parts, into which any thing is 
first divided, should be the largest and most 
general. The resolution of one of these parts 
into others, more minute, is called subdivision. 
So a year is first divided into months. Month 
is then subdivided into weeks ; week, into 
days, and so on. Needless subdivisions should 
be avoided, as thev burden the memory, and 
introduce confusion.* 



CHAPTER THIRD, 
generjVl. description of propositions. 

47. A proposition is a verbal representation 
of some perception^ actj or affection of the mind. 

* LocKe, Essay, b. iii. Watts, Logick, part i. Kirwan, Logick, 
parti. 



44 PROPOSITIONS. 

The constituent parts of a proposition are the 
subject, the predicate, and the copula. The 
two first are called terms, because they are 
the extremes of the proposition ; and they may 
consist of a single word each, or of a collection 
of words, representing some person, thing, or 
attribute. 

48. The subject of a proposition is that, con- 
cerning ivhich something is either asserted, de- 
nied, commanded, or inquired. The predicate is 
that, which is asserted, denied, commanded, or 
inquired, concerning the subject. The copula is 
that, by which the other two parts are connected. 

Body is divisible. 
Man is not omniscient. 
Be ye filled. 
Is Caesar dead ? 

Body, man, ye, and CcBsar, are the subjects of 
these four propositions ; divisible, omniscient, 
filled, and dead, are the predicates ; is, is not, 
and be, the copulas. In the first example, the 
agreement between the subject and predicate 
is asserted ; in the second, it is denied ; in 
the third, it is ordered ; in the fourth, it is 
inquired for. 



PROPOSITIONS. 45 

49. One part of a proposition is often con- 
tained in another. In the following examples, 
the copula is contained in the predicate : 

I think. 

The sun rises. 

These imply, 

I am thinking. 
The sun is rising. 

So the copula sometimes includes the whole, 
or a part of the predicate ; as, Troy was ; that 
is, Troy was existent. The copula is always 
some inflection of the verb to &e, either express- 
ed or understood. 

A single word may contain a complete pro- 
position. Thus scriho implies ego sum scrihens^ 
I am writing. So rejoice^ attend^ imply be thou 
rejoicing ; he thou attentive. 

50. The subject of the proposition usually 
stands first, and the predicate last ; but this 
order is sometimes inverted, as in the following 
example : 

In China are many ingenious artists. 

That is, 

Many ingenious artists are [existent] in China. 



46 PROPOSITIONS. 

The words, which constitute the two terms, 

are sometimes so blended together, that the 

whole, or a part, of one is placed between parts 

of the other. In the following example, the 

whole subject intervenes between parts of the 

predicate : 

" But too often diiFerent is rational conjecture from 
melancholy fact." Burke, 

In imperative and interrogative propositions, 
the copula is usually placed first. As, 

Be thou faithful. 

Is the controversy settled ? 

51. An identical proposition is one, whose 
subject and predicate are composed of the same 
word or ivords, and express precisely the same 
idea. Sometimes the terms are the same, and 
the ideas different. Thus, ho7ne is home. This 
proposition is not identical ; for home, as sub- 
ject, means only a place of residence ; but as 
predicate, it denotes that it is an agreeable 
residence. Sometimes the terms are different, 
but express the same idea. Thus, three times 
three are niiie ; twelve is the ffth part of sixty. 
Here the terms are reciprocal, and may be 
substituted for each other ; but the propositions 
are not strictly identical. 



PROPOSITIONS, 47 

CHAPTER FOURTH. 

SIMPLE, COMPLEX, AND MODAL PROPOSITIONS. 

52. A simple proposition is one^ whose sub- 
ject and predicate are composed of simple terms. 

[See No 27.] As, 

Time is precious. 
Virtue will be rewarded. 

A complex proposition has one or both of its 
terms complex. They are formed in different 
ways. A proposition is sometimes rendered 
complex, by having for its subject or predicate 
some other proposition, or words equivalent. 
Thus, 

That one man should be punished for the crimes of 
another is unjust. 

The words, which precede is^ and which form 
the subject of this example, obviously contain 
an entire proposition. 

53. Frequently the subject of a proposition 
is first represented by the pronoun it^ and after- 
wards distinctly expressed ; as in the following 
expression : 

" It is impossible to guess at the term, to which our 
forbearance would have extended."* 

* Burke, Regicide Peace. 



48 PROPOSITIONS. 

The words, constituting the real subject, 
are here represented by the word it, which 
being discarded, and the subject stated first, 
the proposition will stand thus : 

To guess at the term, to which our forbearance would 
have extended, is impossible. 

64. Another manner of rendering a proposi- 
tion complex is by introducing the pronoun 
whOj ivhich, or that, for the purpose of explain- 
ing the subject or predicate. Thus, 

Cyrus, who founded the Persian empire, was the son 
of Cambyses. 

The words, introduced by the relative, form a 
complete proposition, which is called the in- 
cident ; and the whole proposition, including 
this, is called, in reference to it, primary, or 
principal. As the design of the incident prop- 
osition is purely to explain the subject or 
predicate of the primary, it can be considered 
only as a part of the term, in which it is 
placed. 

55. Lastly, any proposition is complex, 
whose subject or predicate is defined, by an- 
nexing to it a word of limitation, or restriction. 
As, 



PROPOSITIONS. 49 

Upright men are respected. 
The mind is a simple substance. 

The subject of the first example is defined by 
the word upright ; and the predicate of the 
second, by the word simple. These words re- 
strain the latitude of the general terms, men and 
substance^ to which they are joined. They 
are equivalent to incidental propositions, and 
may be readily resolved into them. Thus, 

Men, who are upright, are respected. 
The mind is a substance, that is simple. 

56. A modal proposition is one^ whose copula 
is qualified hy some ivord or ivords^ representing 
the manner of the agreement or discrepancy 
between the subject and predicate. The modal- 
ity of propositions is frequently expressed by 
the auxiliary verbs, may^ can^ must^ ought^ and 
the hke, which imply possibility, necessity, or 
contingency. Thus, 

Men of influence can do much good. 
Subordination must be maintained. 

The thing asserted, in each of these proposi- 
tions, is not the simple and absolute agreement 
of the subject with the predicate, but barely 



60 QUALITY AND QUANTITY 

the nature of that agreement ; namely, that it 
is possible or necessary.* 



CHAPTER FIFTH. 

QUALITY AND QUANTITY OF PROPOSITIONS. 

57. Propositions are further distinguished 
into affirmative and negative ; which has been 
called a distinction with respect to quality. In 
affirmative propositions^ the predicate and subject 
are asserted to agree. As, 

Clevis was the founder of the French monarchy. 

In negative propositions^ the predicate is de- 
clared to he incompatible ivith the subject. This 
is commonly done by placing the negative par- 
ticle not immediately after the copula. Thus, 

The world is not eternal. 

58. Sometimes the negative particle is placed 
so far from the copula, that it appears to have 
no immediate connexion with it ; but rather to 
belong to some other part of the proposition : 

Not all the troops united were able to defend the 
fortress. 

* Watts, Logick, part ii. ch. 2. Kirwan, Logick, part i. ch. 2. 



OF TROPOSITIONS. 61 

Here the negative word is placed before the 
subject ; but still its influence falls wholly on the 
copula, and makes the proposition signify the 
opposite of what it would without it. This 
will be made evident by stating the proposition 
thus, 

All the troops united were not able to defend the 
fortress. 

59. By the quantity of a proposition is meant 
its consideration in respect to the extent of its 
subject ; and according as the subject is used 
in the whole or a part of its extension, propo- 
sitions are denominated universal or particular, 
A universal proposition is one^ whose subject is 
a general term, used in the whole of its extension. 
The signs of universality are aZ/, each^ every^ 
no^ neither^ and the like. Thus, 

All free agents are accountable. 

Every sin is a violation of the Divine law. 

These are universal propositions ; because each 
subject includes an extensive class, to each 
individual of which the predicate is declared 
applicable. 

60. When the sign of universality is omit- 
ted, or the indefinite article is placed before 



52 QUALITY AND QUANTITY 

the general subject, the proposition is called 
indefinite. Thus, 

Planets are continually changing their places, 

A just sovereign regards the welfare of his subjects 

These subjects are taken in their greatest 
extent ; for if there were any planet, that did 
not change its place, or any just sovereign, 
who neglected the welfare of his subjects, the 
propositions would not be true. 

61. A particular proposition is one^ whose 
subject is a generdl term, but is taken only in a 
part of its extension. The signs of particular- 
ity are some, many, most, several, few, and the 
like. 

Some animals are amphibious. 
Many buildings were destroyed. 

The words, some and many, restrain the sub- 
jects, animals and buildings, and intimate, that 
a part only of the individual beings, which they 
include, will admit the predicates, amphibious 
and destroyed. 

62. A proposition, whose subject is the 
proper name of some individual person or 
thing, is denominated singular. As> 



OF PROPOSITIONS. 53 

Alfred founded the University of Oxford. 
Stagira was the birthplace of Aristotle. 

A definitive pronoun, placed before the sub- 
ject of a proposition, renders it singular. As, 

That general was defeated. 

The subject of a singular proposition, as it 
represents only an individual, is necessarily 
taken in its whole extension ; for which reason 
singular propositions are classed with universal. 
Every proposition, therefore, is either universal 
or particular. 

63. Besides this quantity in the subject, 
there is another quantity in the predicate of 
a proposition ; for this, as well as the subject, 
is taken either in the whole, or only in a part 
of its extension. The quantity of the subject 
and that of the proposition are the same ; for 
in every uiiiversal proposition^ the subject is 
universal ; and in every particular proposition^ 
the subject is particular. But the quantity of 
the predicate depends on the quality of the 
proposition. [See No. 57.] In all affirmative 
propositions the predicate is particular ; and in 
all negative propositions it is universal. 
6* 



64 QUALITY AND QUANTITY 

64. The predicate of an affirmative propo- 
sition, separately considered, is commonly a 
more general term than the subject. It is 
usually a genus, of which the subject is a spe- 
cies. But, when united to the subject, no 
greater extension is attributed to it than is 
just sufficient to enable it to embrace the 
subject. It is taken in the whole of its 
comprehension, but in a part only of its ex- 
tension. [See No. 35.] For example. 

Every dog is an animal. 

Here it is barely asserted, that the predicate, 
animal^ does extend so far as to include every 
individual of the subject, dog ; but it is neither 
asserted nor denied, that it is susceptible of 
a greater extension. Now, though the term, 
a7iimal, separately considered, is applicable to 
millions of beings besides dogs, still, in this 
place, it has no more extension than is express- 
ly given it by the words of the proposition. 
The predicate of every affirmative proposition 
being in this way restrained by its subject, 
universality can never be attributed to it. 

65. But in negative propositions, the predi- 
cate, not being restrained by a subject, to which 



OPPOSITION AND CONVERSION BB 

it is declared inapplicable, is taken in the 
whole of its extension. Thus, 

No animal is a tree. 

This proposition implies, that the things^ 
included under tree^ are so dissimilar to those, 
included under animal^ that no individual can 
be found, to which the two terms will apply. 



CHAPTER SIXTH. 

OPPOSITION AND CONVERSION OF PROPOSITIONSe 

60. Opposition in propositions implies a dis- 
agreement in respect of quality^ Two proposi- 
tions, which have the same subject and the 
same predicate, are said to be opposite, when 
one absolutely denies, in whole or in part, 
what the other affirms. There are three ways, 
in which propositions of this sort m.ay be 
opposed. First, a universal affirmative may 
be opposed to a particular negative. These 
are called contradictory. As, 

Every defensive war is just. 
Some defensive wars are not just. 

Secondly, a universal affirmative proposition 
may oppose a universal negative. These are 
called contrary. As, 



56 OPPOSITION AND CONVERSION, 

Every disease is contagious. 
No disease is contagious. 

Thirdly, a particular affirmative may be oppos- 
ed to a particular negative. These are called 
subcontrary. As, 

Some amusements are innocent. 
Some amusements are not innocent. 

Two contradictory propositions can never 
be either both true, or both false, at the same 
time ; two contraries may be both false, but 
they cannot be both true ; and two subcontra- 
ries may be both true, but they cannot be both 
false, at the same time. 

67. The conversion of a proposition is the 
transposition of its terms^ so that the subject shall 
take the place of the predicate^ and the predicate 
the place of the subject^ ivith the preservation of 
truth. When the subject and predicate simply 
change places, without causing any alteration 
in the quantity of the propositions, it is called a 
simple conversion. But if, in the new arrange- 
ment, a term of particularity is introduced, to 
restrain the subject of the derivative propo- 
sition within the same extension, which it had 
as predicate of the original, this is called a 
particular conversion ; by the schoolmen it was 



OF PROPOSITIONS. 57 

denominated conversio per accidens. Universal 
affirmative propositions are usually convertible 
only in the latter mode ; but universal negatives 
and particular affirmatives are convertible in 
the former. 

68. The converse of a universal affirmative 
proposition must, generally speaking,^ be a 
particular affirmative. It is necessary that 
both the terms be taken in exactly the same 
extension, in both arrangements ; and since, by 
the rule stated in No. 63, the predicate of the 
original proposition must be particular, this 
same term must be particular in the converse, 
where it is made the subject, which will there- 
fore render the proposition particular. Thus, 

Orig, Prop, All swallows are birds. 
Converse. Some birds are swallows. 

69. The converse of a universal negative 
proposition is a universal negative. The sub- 
ject and predicate, being of equal extent, mu- 
tually exclude each other ; and as these terms 

* This is always the case, except in those propositions, whose 
predicate is a complete definition of the subject. In such proposi- 
tions, the subject and predicate are reciprocal terms. As^ four times 
five are twenty ; and twenty are four times five. fVine is the juie§ 
of the grape ; and the juice of the grape is wine. 



58 OPPOSITION AND CONVERSION. 

are both universal in the first arrangement, 
[See No. 65.'] they must be so in the second. 
Thus, 

Grig, Prop. No deer is an elephant. 
Converse, No elephant is a deer. 

70. Particular affirmative propositions are 
convertible only into the same. In these the 
terms are both particular ; [See No. 61, 63.] 
and they can never become otherwise by a 
new arrangement. Thus, 

Grig, Prop, Some birds lie dormant during the winter. 
Converse, Some beings, that lie dormant during the 
winter, are birds. 

71. A particular negative proposition is 
inconvertible in anjr mode. Its subject is par- 
ticular, and by conversion this subject would be 
made the predicate of a negative proposition, 
and must therefore be universal, according to 
No. 65 ; a whole deduced from a part, which 
is impossible. For example ; from this propo- 
sition. 

Some birds are not swallows. 

we cannot affirm this. 

No swallows are birds. 

This would be to deduce a whole from a part ; 



COMPOUND PROPOSITIONS. 59 

since stvallow is denied of a part only of the 
extension of bird, in the first proposition ; and 
of the whole of it, in the last.^ 

72. There is a third species of conversion, 
in which a negative particle is inserted both 
in the subject and predicate' of the derivative 
proposition, unless previously included in the 
original. This is denominated conversion by 
contraposition. Thus, 

Orig. Prop. Every bird is an animal. 

Converse, That, which is not an animal, is not a bird. 

These negatives destroy each other, and the 
proposition is considered as affirmative.! 



CHAPTER SEVENTH. 

COMPOUND PROPOSITIONS. 

73. A compound proposition is one, which has 
two or more subjects, or predicates, or both ; and 
may be resolved into two or more propositions. 

* In a universal affirmative proposition, the subject only is 
universal, and the predicate particular ; in a universal negative, the 
subject and predicate are both universal ; in a particular affirmative, 
the subject and predicate are both particular ; and in a particular 
negative, the subject only is particular, and the predicate universal. 

f Watts, Logick, part li. ch. 2. Kirwan, Logick, part i. ch. 3. 



60 COMPOUND PROPOSITIONS. 

As, 

Spring, summer, autumn, and winter, are seasons of 
the year. 

Alfred was prudent, valiant, just, and benevolent. 

As the four subjects of the first example are 
separately applicable to the predicate, seasons 
of the year J and the four predicates of the last, 
separately applicable to the subject, Alfred, 
each may be resolved into four propositions. 
Thus, 

Spring is a season of the year. 
Summer is a season of the year, &c. 

74. Every compound proposition may be 
reduced to as many single ones as it contains 
subjects, to which the whole predicate will 
apply, and predicates, to which the whole sub- 
ject will apply ; or as there are parts in each, 
which are separately applicable to each other. 

Beasts, birds, and insects, have life, sense, and motion. 

This example contains three subjects and three 
predicates, and may be reduced to nine distinct 
propositions. 

75. Two or more words are sometimes so 
coupled together in the subject or predicate, 
as to give the proposition the appearance of 



COMPOUND PROPOSITIONS. 61 

being compound, when it is single. Thus, 

Joy and sorrow are opposite qualities. 
Ye cannot serve God and Mammon. 

These are complex propositions, but they are 
not compound ; for neither" of them can be 
resolved into two propositions. The two parts, 
which make up respectively the subject of the 
one and the predicate of the other, must be 
taken conjointly* 

76. Compound propositions may be distin- 
guished from those, that are barely complex, 
by the following circumstances. First, in a 
compound proposition, the parts, which con- 
stitute the subject or predicate, are independent 
of each other, and may be taken separately, 
as well as conjointly ; which is not the case 
in complex propositions. In the latter, either 
certain words are joined together, which re- 
present integral parts of some whole, that is to 
be the subject or predicate, as, three and sevem 
are equal to ten ; or one part of the proposition 
is repeated, directly or implicitly, by some 
relative word, as, it^ that^ ivho, which ; or, lastly, 
the real subject or predicate is defined by an 
explanatory word. In either of these cases, 
6 



62 COMPOUND PROPOSITIONS. 

the words, which render the proposition com- 
plex, must be regarded as real parts of the 
term, in which they occm\ 

77. Secondly, wherever a complex proposi- 
tion involves a simple one, there will be the 
distinction of primary and incidental ; and the 
incidental proposition may be false, while the 
primary is true. But, in compound proposi- 
tions, there exists no distinction of primary and 
incidental, each part being independent of the 
rest ; and the compound proposition must be 
false, when any one of the propositions, it in- 
volves, is false, though the others be true. 

78. Compound propositions are, in most 
books of logick, distributed into various sorts, 
denominated copulative^ disjunctive^ conditional^ 
causal^ relative^ and discretive ; which denom- 
inations are taken from the particle, employed 
in the composition of their subject or predicate 
The examples, already given, belong to the 
first class. 

A disjunctive proposition asserts, that a sub- 
ject agrees with one of tivo or more named pred- 
icates, or a predicate with one of two or more 
subjects enumerated ; but does not specify ivhich. 



COMPOUND PROFOSITIONS. 63 

Thus, 

Either the sun or the moon will be eclipsed, on Christ- 
mas day. 

The weather will, at that time, be either clear or 
cloudy. 

79. A discretive proposition consists of tivo 
parts^ which are contratsed by reason of some 
apparent opposition or inconsistency^ intimated 
by the particles but, though, notwithstanding, 
a7id the like. iVs, 

Hannibal, though unfortunate, was a great general. 
A man may deceive his neighbour, but not his God. 

80. The other distinctions of this class are 
incorrect. What are usually termed condi- 
tional^ causal, and relative propositions, are 
nothing moro than different modes of connect- 
ing two entire propositions together. It is 
essential to the individuality of a proposition, 
that it have but one copula. However com- 
pounded or complicated the subject or predicate 
may be, they must be connected by a single 
affirmation or negation. This rule is violated 
in every instance of what are called condition- 
al, causal, and relative propositions. The 
following have been given as examples of 
these kinds : 



64 COMPOUND PROPOSITIONS. 

If the sun be fixed, the earth must move. 
Rehoboam was unhappy, because he followed evil 
counsel. 

As is the Father, so is the Son. 

The first is given as an example of a condition- 
al^ the second, of a causal^ and the third, of a 
relative proposition. But no one of them can 
with any propriety, be considered as a com- 
pound proposition. Each example consists 
of two entire propositions, possessing distinct 
subjects, copulas, and predicates ; and so put 
together as to constitute a complete act of 
ratiocination*^ 

* Collard, Logick, part iii. ch. 2. Kirwan, Logick, part i. ch. 4. 
Watts, Logick, part ii. ch. 2. 



PART THIRD. 



OF JUDGMENT AND REASONING. 



CHAPTER FIRST. 

INTUITIVE EVIDENCE, 



81. Judgment is an act of the mind^ uniting 
or separating tivo objects of thought according 
as they are perceived to agree or disagree. The 
relation between these objects is sometimes 
discovered by barely contemplating them, with- 
out reference to any thing else ; and sometimes 
by comparing them with other objects, to which 
they have a known relation. The former is 
simple comparison ; the latter is an act of 
reasoning. The determination of the mind in 
both cases is denominated judgment. Every 
act of judgment is grounded on some sort of 
evidence. That, which determines the mind in 
simple comparison, is called intuitive evidence ; 
and that, which is employed in reasoning, 
deductive. 



66 INTUITIVE EVIDENCE, 

The principal kinds of intuitive evidence, oi 
sources of intuitive belief, are the evidence 
of sense^ of conscwusness^ of memory^ and of 
axioms^ or general principles. 

82. The first source of intuitive belief is the 
festwiony of the external senses^ hearing, seeing, 
touching, smelliog, and tasting. These organs 
come to their usual degree of maturity in in- 
fancy, and are employed with equal confidence 
by all descriptions of people. Men have, in 
every country, and in every period of the 
world, been governed by their testimony, even 
in their most important conceras. We can 
no more question the existence of the bodies, 
which we see and handle, than we can our own 
existence, or the truth of the most obvious 
maxim, that can be proposed to our thoughts. 
On the evidence of the senses is grounded all 
our knowledge of the nature^ powers, and qual- 
ities of the material objects around us. All 
truths relative to physical science or to the 
events of history, and all those rules of prudence, 
which relate to the preservation and health of 
our bodies, must ultimately be resolved into 
this principle, that things are as our senses 
represent them. 



INTUITIVE EVIDENCE. 67 

83. Consciousness is another source of in- 
tuitive evidence. Its office is to inform us of 
the present existence of our various passions, 
affections, and mental operations. The whole 
science of the human mind is built on this evi 
dence ; and no branch of knowledge stands on 
a surer foundation ; for no evidence is superioi 
to this, where it is completely ascertained. 
But it is sometimes difficult to define precisely 
the subjects of our consciousness. Those, who 
have not been accustomed to attend to their 
intellectual operations, are liable to err in apply- 
ing this evidence. I think, compare, reason, 
doubt ; I feel pain, or pleasure ; I remember 
past events. These are facts, of which I am 
conscious, and of which I am unable to ques- 
tion the reality. The power of consciousness 
iS exercised but imperfectly, till the mind 
advances towards maturity. Some^ have 
supposed it to be wholly dormant during the 
years of childhood. It is however exercised, 
in a greater or less degree, by people of all 
classes ; and the subjects, about which it is 
employed, can be no other than the mental 
states of a being, which each one calls himself. 

* Scott, Intellectual Philosophy. 



68 INTUITIVE EVIDENCE. 

84. As the evidence of sense furnishes us 
with the knowledge of things present in the 
material world, and the evidence of conscious- 
ness informs us of whatever is passing in our 
own minds ; so the evidence of memory gives 
us immediate knowledge of things past, whether 
of a material or intellectual kind. This 
evidence has ever commanded the belief of 
mankind as effectually as that of sense. Past 
facts and occurrences, of which we have a clear 
remembrance, are regarded as certain. This 
is implied by men in all their efforts to gather 
knowledge and improvement from their past 
experience. It is on this principle, that causes, 
which involve the lives and fortunes of men, 
are decided by the testimony of witnesses, in 
courts of justice. Propositions, formerly prov- 
ed, may be relied on as present knowledge, 
though the reasons, which first gained our 
assent to them, be now forgotten, provided we 
remember that we once carefully investigated 
them, and were then certain of their truth. 
Such propositions must often be introduced or 
referred to in demonstrations ; and, should 
doubts be entertained respecting their truth, 
they must weaken our confidence in the con- 



INTUITIVE EVIDENCE. 



69 



elusions, to which they are subservient. Unless 
therefore the evidence of memory be admitted 
as a ground of certain knowledge, the founda- 
tion of demonstrative reasoning would be 
destroyed. 

85. Another species of intuitive evidence is 
that, which accompanies mathematical axioms 
and all those abstract truths, which carry their 
own evidence with them, and are readily as- 
sented to, as soon as they are contemplated. 
Thus, the ivhole is greater than a part. Things 
equal to the same are equal to one another. 
Every effect must have a cause. These prop- 
ositions force our assent by irresistible evi- 
dence, as soon as we understand the terms, by 
which they are expressed. They cannot be 
proved ; because no principles more evident 
can be assumed, from which their truih could 
be deduced. In all demonstrative reasoning, 
constant use is made of these abstract and 
self-evident propositions.* 

* Beattie, Essay on Truth, part i. ch. 2. Stewart, Elem. vol. ii. 
ch. 1. Campbell, Phil. Rhet. vol. i. ch. 5. Scott, Elem. Intel. PhiL 
ch. 8, sect, 3. 



70 DEDUCTIVE EVIDENCE. 



CHAPTER SECOND. 

DIFFERENCE BETWEEN MORAL AND DEMONSTRATIVE 

REASONING. 

86. Reasoning is a process^ by which un- 
known truths are inferred from those^ ivhich are 
already known or admitted. The evidence, 
employed in reasoning, is deductive^ and is dis- 
tinguished into two kinds, which are, moral 
and demonstrative. Moral evidence is that 
species of proof ivhich is employed on subjects, 
directly or indirectly connected loith moral con- 
duct. It is not however confined to such sub- 
jects ; but is extended to all those facts and 
events, concerning which we do not obtain the 
evidence of sense, intuition, or demonstration ; 
and to all the general truths, Tvhich are de- 
duced from observation and experience.^ De- 
monstrative evidence is that^ by ivhich ive trace 
the relations^ subsisting among thhigs, in their 
nature immutable, like the subjects of geometry 
and arithmetick. On this distinction of deduc- 
tive evidence is founded the most general divi- 
sion of reasoning, which is into moral or proba- 

* Gambler, Moral l^videncc, ch. L 



DEDUCTIVE EVIDENCE. 71 

hle^ and demonstrative. The principal differences 
in these modes of reasoning are the following : 

87. First, they differ in regard to their sub- 
jects. Demonstration is employed about ab- 
stract and independent truths, or those rela- 
tions, which are considered as necessary, and 
whose subjects may be exactly measured and 
defined. The properties of number and quan- 
tity are of this sort. They have no respect to 
time or place ; depend on no cause ; and are 
subject to no change. But the subjects of 
moral reasoning are matters of fact, which 
are in their nature contingent, and the varia- 
ble connexions, which subsist among things in 
actual existence. Thus, that mercury may he 
congealed ly cold^ that lead is fusible^ that 
Hannibal led an army over the Alps^ that Lisbon 
was once destroyed by an earthquake^ and the 
like, are truths within the province of moral 
reasoning. 

88. Secondly. In a demonstration, it is not 
necessary to examine more than one side of 
the question ; for if any proposition be demon- 
strated to be true, whatever can be offered, as 
proof, on the opposite side, must be mere fal- 
lacy. But in cases of moral reasoning, there 



72 DEDUCTIVE EVIDENCE. 

are frequently arguments of weight on both 
sides ; and therefore, in order to judge cor- 
rectly, we must consider each side of the 
question, and give our assent to that, on which 
there appears the greatest weight of evidence. 
Thus, having demonstrated the equality of the 
three angles of a triangle to two right ones^ 
there is no need of inquiring what may be 
urged against the demonstration. But the 
case is different in questions of a moral kind, 
as whether falsehood may he practised towards 
an assassin ; or ivhether an oath^ extorted by 
violence, be obligatory. In such questions, the 
mind is often perplexed, and the judgment 
held in suspense by the conflict of opposite 
reasons. 

89. Thirdly. Propositions, contrary to those 
established by moral evidence, are merely 
false ; but those, which are contrary to de- 
monstrated propositions, are not only false, but 
likewise absurd. Thus, the assertion, that 
Carthage was never taken by the Romans, 
though false, is not absurd ; for there was a 
time, when it was true. But the assertion, 
that the opposite angles, formed by two straight 



DEDUCTIVE EVIDENCE. 73 

lines crossing each other, are not equals is not 
only false, but also absurd- 

90. Fourthly. In demonstration there are no 
degrees ; the conclusion resulting necessarily 
from the definitions and principles, which have 
been assumed as the basis .of the reasoning. 
But in moral reasoning there is often contrariety 
of evidence ; and the degree of assurance, we 
feel in the conclusion, must depend on the 
degree, in which the evidence on one side 
exceeds that on the other. 

91. Fifthly. In every process of demonstra- 
tive reasoning, the proofs are framed into one 
coherent series, each part of which must have 
an intuitive agreement with that, which goes 
before, and with that, which follows it. The 
longest geometrical demonstration is but one 
uniform chain, the links of which, taken sepa- 
rately, are not regarded as so many argu- 
ments ; and consequently, when thus taken, 
they prove nothing. But taken together, and 
in their proper order, they form one argument, 
which is perfectly conclusive. In a process of 
moral reasoning, on the contrary, there is usu- 
ally a combination of many separate arguments, 
in no degree dependent on each other. Each 

7 



74 DEDUCTIVE EVIDENCE. 

possesses some weight, and bestows on the 
conclusion a certain degree of probabihty ; of 
all which, accumulated, the credibility of the 
fact is compounded- Thus, the proof, that the 
Romans once possessed Great Britain^ is made 
up of a variety of independent arguments : as, 
immemorial tradition ; the testimony of histo- 
rians ; the ruins of Roman buildings, camps, 
and walls ; Roman coins, inscriptions, and the 
like. These are independent arguments ; but 
they all conspire to establish the fact. 

92. Sixthly. It may ^e further noticed, that 
the obstacles, which occur in the practice of 
these two modes of reasoning, are of different 
kinds. Those, which impede our progress in 
demonstration, arise from the large number of 
intermediate steps, and the difficulty of finding 
suitable media of proof. In moral reasoning, 
the processes are usually short, and the chief 
obstacles, by which we are retarded, arise from 
the want of exact definitions to our words ; the 
difficulty of keeping steadily in view the vari- 
ous circumstances, on which our judgment 
should be formed ; and from the prejudices 
arising from early impressions and associa- 
tions. 



DEDUCTIVE EVIDENCE. 75 

93. It should be remarked here, that the 
epithet probable^ as appUed by logicians to the 
evidence of moral reasoning, has a technical 
meaning, altogether different from its usual 
signification. In common discourse, it is ap- 
plied to evidence, v^hich does not command a 
full assent ; but in logical discussions, it has a 
more comprehensive meaning, not only includ- 
ing every subordinate degree of moral evidence, 
but also the highest. In this latter sense, it is 
not to be considered as implying any deficiency 
of proof, but as contradistinguishing one species 
of proof from another ; — not as opposed to v\^hat 
is certain, but to what may be demonstrated 
after the manner of mathematicians ; — not as 
denoting the degree of evidence, but its nature. 
It is the more important to keep in mind this 
distinction betv^een the popular and technical 
meaning of the term probable^ as the neglect 
or misapprehension of it has given origin to 
a distrust of moral reasoning, as inferior in 
evidence to mathematical demonstration ; and 
induced many authors to seek for a mode of 
proof altogether unattainable in moral inquiries; 



76 INDUCTION. 

and which, if it could be attained, would not 
be less liable to the cavils of scepticks.* 



CHAPTER THIRD. 

INDUCTION. 

94. The first kind of moral reasoning is that, 
by which we infer general truths from partic- 
ular facts, that have fallen under our observa- 
tion. This has been called the method of 
induction. It is founded on the belief, that the 
course of nature is governed by uniform laws, 
and that things will happen in future, as we 
have observed them to happen in time past. 
We can have no proof of a permanent connexion 
between any events, or between any two qual- 
ities either of body or mind. The only reason 
for supposing such a connexion in any instance 
is, that we have invariably found certain things 
to have been conjoined in fact ; and this expe- 
rience, in many cases, produces a conviction 
equal to that of demonstration. 

95. When a property has been found in 

* Reid, Intellectual Powers, essay vii. ch. 3. Campbell, Phil 
Rhet. b. i. ch. 5. sect. 2. Gambler, Mor. Evid. ch. 1. Stewart, 
Elem. Phil, of Mind, vol. i. Introd. part ii. sect. 2. vol. ii. ch. 2. seet. 4 



INDUCTION. 77 

many subjects of a similar kind, and no con- 
tradictory instance has been discovered, though 
diligently sought, we have an irresistible per- 
suasion, that the same property belongs to all 
the individuals of that class. Thus, having 
applied a magnet to several masses of iron, and 
found uniformly a strong attraction to take 
place, we feel no doubt, that it belongs to the 
nature of iron to be thus affected by that 
substance ; and, though our experience reaches 
only to a small part of the masses of iron in 
existence, we assert with confidence, that all 
iron is susceptible of magnetical attraction. 
So, having often noticed, that, by the applica- 
tion of heat to a certain degree, water is made 
to boil, and that, in the absence of heat to 
a certain degree, it becomes congealed ; and 
having ascertained these changes to be uniform, 
so far as they have been observed by ourselves 
and others, we readily ascribe them to the 
nature of water, and conclude, that in every 
country water will boil or freeze, on being ex- 
posed to those opposite degrees of temperature. 
96. In this way, by observations and experi- 
ments on individuals of a similar kind, noticing 
with exactness their agreement, or the circum- 



78 INDUCTION. 

Stances, in which they differ, we obtain general 
truths relating to the properties and laws of 
material objects. By the same inductive pro- 
cess we investigate the laws, which govern the 
phenomena of mind. Thus, from experience, 
it has been ascertained, that, v/hen two ideas 
have been often presented to the mind in 
immediate succession, they acquire a tendency 
mutually to suggest each other ; so that, when 
either of them occurs to our thoughts, the other 
readily follows it. We learn also from ex- 
perience, that the durabiUty of past impressions 
on the mind depends greatly on the attention, 
with which they were at first received. From 
the uniformity of these facts we are taught, 
that contiguity in time or place is a principle of 
association ; and that attention is necessary to 
memory. 

97. As we deduce the common properties of 
a single class of beings from observations on 
individuals of that class, so, by comparing 
individuals of different classes, we discover 
important resemblances between one species 
and another, and are enabled to obtain more 
extensive conclusions. Thus, having seen the 
milk of several animals of different species, and 



INDUCTION. 79 

found it uniformly to be white, we conclude, 
that the milk of all animals is so. In like man- 
ner, having witnessed the effect of jfire on 
several pieces of gold^ iron^ lead, and so forth, 
we affirm, that all metals are fusible. In this 
way, beginning with individuals, we ascend to 
species ; and thence proceed from less general 
to more general conclusions, till we arrive at 
those abstract propositions, which are called 
axioms or general truths. 

98. This method of induction is recommend- 
ed by Lord Bacon, as the first and most im- 
portant instrument of reason, in its search after 
truth. We employ it not only in the investi- 
gation of general truths, relating to things in 
actual existence ; but in gaining those practi- 
cal rules and maxims, by which the common 
business of hfe is carried on. 

99. The use of induction, in learn ng the 
signification of words, is thus happily explained 
by Mr. Stewart : " A familiar illustration of 
" this process presents itself in the expedient, 
^* which a reader naturally employs for deci- 
" phering the meaning of an unknown word, in 
" a foreign language, when he happens not to 
*^have a dictionary at hand. The first sen- 



? 



80 INDUCTION. 

'^ tence, where the vv^ord occurs, affords, it is 
^'probable, sufficient foundation for a vague 
'' conjecture concerning the notion, annexed 
" to it by the author ; some idea or other being 
" necessarily substituted in its place, in order 
'' to make the passage at all intelligible. The 
" next sentence, where it is involved, renders 
''this conjecture a little more definite ; a third 
" sentence contracts the field of doubt within 
"still narrower hmits ; till at length a more 
" extensive induction fixes completely the sig- 
" nification we are in quest of. There cannot 
'' be a doubt, I apprehend, that it is in some 
'' such way as this, that children slowly and 
" imperceptibly enter into the abstract and com- 
'' plex notions, annexed to numberless words in 
" their mother tongue, of which we should find 
" it difficult, or impossible, to convey the sense 
''by formal definitions.''^ 

100. In another place, Mr. Stewart has 
described the manner of using induction, in 
tracing an event to its physical cause : "As 
" we can, in no instance, perceive the link, by 
" which two successive events are connected, so 

* Philosophical Essays, essay v. ch. 1. 



INDUCTION. 8 1 

^* as to deduce, by reasoning a priori^ the one 
'^ from the other, as a consequence or effect, 
^' it follows that, when we see an event take 
" place, which has been preceded by a com- 
" bination of different circumstances, it is im- 
'' possible for human sagacity to ascertain, 
" whether the effect is connected with all the 
" circumstances, or only with a part of them ; 
'' and, on the latter supposition, which of the 
" circumstances is essential to the result, and 
^' which are merely accidental accessories or 
' concomitants. The only way, in such a case, 
'* of coming at the truth, is to repeat over the 
-^ experiment again and again, leaving out all 
'' the different circumstances successively, and 
*' observing with what particular combinations 
'' of them the effect is conjoined. 

"When, by thus comparing a number of 
" cases, agreeing in some circumstances, but 
" differing in others, and all attended with the 
''same result, a philosopher connects, as a 
" general law of nature, the event with its 
'^ physical cause^ he is said to proceed according 
'• to the method of induction.^'^^ 

* Elements of the Philosophy of the Mind, vol. ii. ch. 4. sect. 1. 



82 INDUCTION. 

101. Inductive conclusions will amount to 
moral certainty, whenever our experience has 
been uniform, and the number of cases examin- 
ed sufficiently numerous. But this reasoning 
is liable to be fallacious through impatience 
in the investigation, by which judgments axe 
hastily formed, without a sufficient accumu- 
lation of facts. The number of instances, 
required to justify a general conclusion, must 
be increased in proportion as the facts, from 
which we reason, are more irregular in their 
appearance. In judging concerning the prop- 
erties of inanimate matter, a general inference 
may sometimes be drawn from a small number 
of particular cases. If, for example, aqua 
fortis has been known to dissolve silver in one 
instance, the presumption is very strong, that it 
will do so in all. But the success, which may 
happen to attend a medicine in a single instance, 
furnishes but a slight presumption with regard 
to its general operation on the human body. 

102. When our experience has not been 
uniform, the conclusions we make will fall 
short of moral certainty. An equal number of 
favourable and unfavourable instances leaves 
the mind in a state of suspense, without exciting 



ANALOGY. 83 

the smallest expectation on either side. As 
the ratio, which the instances on the two sides 
bear to each other, may vary indefinitely, so 
must the judgments, founded on them, vary in 
a like degree from the neighbourhood of cer- 
tainty, dovra to that of entire improbability.* 



CHAPTER FOURTH. 

ANALOGY. 

103. Analogy is the foundation of another 
species of moral reasoning, similar in most 
respects to analytical induction. They both 
proceed on the same general principle, that 
nature is consistent and uniform in her opera- 
tions ; so that from similar circumstances similar 
effects may be expected ; and in proportion as 
the resemblance between two cases diminishes, 
the less confidence must be placed in the con- 
clusions, made from the one to the other. The 
word analogy is used with much vagueness. 
Sometimes it denotes only a slight and distant 

* Bacon, Novum Organum, libr i. Campbell, Phil. Rhet. vol. i. 
ch. 5. sect 2. Beattie, Essay on Truth, part i. ch. 2. sect. 6. 
Tatham, Chart and Scale of Truth, vol. i. ch. 4. sect. L Stewart, 
Elem. vol. ii. ch. 4. Gambler, Mor. Evidence, ch. 2. Scott, InteL 
Phil. Appendix, ch. 2. 



84 ANALOGY. 

resemblance ; as that, which is found between 
different species of the same genus. Some- 
times it impUes a correspondence of different 
relations ; as that, which exists between the 
fins of a fish and the wings of a bird ; the 
latter bearing the same relation to the air, that 
the former does to the water. 

104. Inductive and analogical reasoning are 
so similar in their nature, that it is not easy 
to point out their specifick difference. Every 
inductive process commences with analogy. 
The following circumstances appear to mark 
a distinction between them, sufficient to justify 
their being treated as separate articles. First, 
induction is a process from several individuals of 
a class to the whole, .ts conclusions therefore 
are always general. But by analogy we argue 
from one individual being to another of the 
same class ; and from one species to another. 
Secondly, the evidence, employed in analogy, 
is wholly iiidirect and collateral ; — the coexist- 
ence of two qualities in one subject affording 
no direct evidence of their coexistence in any 
other. But in the inductive process we have 
direct evidence, that the property, which we 
apply to a whole class, exists in many individ- 



ANALOGY. 85 

uals of that class. It is true, that in all induc- 
tion analogy must be used ; for we can never 
separately examine every individual of a whole 
class, however cautiously we may proceed. 
So far as w^e extend our observations or 
experiments, the evidence is direct ; but, with 
regard to the remaining subjects of the class, 
the conclusions must rest wholly on analogy. 

105. Analogy is an unsafe ground of reason- 
ing ; and its conclusions should seldom be 
received, without some degree of distrust. 
When things resemble each other in several 
important circumstances, we are apt to sup- 
pose the similitude more extensive than it 
really is. The ancient anatomists, being hin- 
dered by their superstition from dissecting the 
bodies of men, endeavoured to obtain the 
information, which might thence have been 
derived, from those quadrupeds, whose internal 
structure was thought to approach nearest to 
that of the human body. In this way they were 
led into numerous mistakes, which have been 
detected by the anatomists of modern times. 

106. The following is stated by Dr. Reid 
as an example of analogical reasoning : ^' We 
'' observe a great similitude between this earth, 

8 



86 ANALOGY. 

"which we inhabit, and the other planets, 
" Saturn, Jupiter, and so forth. They all re- 
"?olve round the sun, as the earth does: 
" though at difierent distances and in diflerent 
" periods. They borrow all their hght from the 
'• sun, as the earth does. Several of them are 
•' known to revolve round their axes, hke the 
" earth, and by that means must have a like 
" succession of day and night. Some of them 
" have moons, that serve to give them light. 
" in the absence of the sun, as our moon does 
'• to us. They are all in their motions subject 
" to the same law of gravitation as the earth 
" is. From all this similitude it is not unrea- 
"sonable to think, that those planets may, 
^' like our earth, be the habitation of various 
"orders of hving creatures.*'* 

In the same manner we may conclude from 
analog}', that the comets are inhabited. But 
this conclusion is less probable than the other, 
in the same proportion as the comets have 
less resemblance to this earth, than the planets 
have. 

107. There are many subjects, both specu- 
lative and practical, about which analogy is 

* £8sa3rB on InteDectiud Powers, essay L ch. 4. 



ANALOGY. 87 

the only evidence we can employ. When a 
lawyer is perplexed with a case, that falls not 
fairly within the provisions of any existing 
statute, and for which his file affords no exact 
precedent, he is placed under the necessity of 
tracing remote analogies and correspondences 
between this case and others within his knowl- 
edge, and of forming his method of procedure 
by the equivocal evidence, furnished by such 
an investigation. To reason correctly on sub- 
jects of this nature often requires more caution 
and discrimination, than are usually required 
in reasoning on the evidence of testimony or 
experience. " It is by the urging of different 
" analogies, that the contention of the bar is 
*' carried on ; and it is in the comparison, 
" adjustment, and reconciliation of them with 
"one another, that the sagacity and wisdom 
"of the court are seen and exercised.''^ 

108. Analogy, on account of the uncertainty 
which attends its conclusions, is rarely employ- 
ed in scientifick investigations. It serves to 
guide our judgments, where direct evidence 
cannot be obtained ; and it affords a degree 
of probability, which is sufficient for the prac- 

*^ Paley, Polit. Phil. ch. 8. 



88 REASONING ON FACTS, 

tical business of life. The proper use of this 
instrument is to defend and illustrate truths, 
already admitted on other evidence. It assists 
to explain ambiguities of language, and to 
exhibit obscure truths in a clear and familiar 
light.^ 



CHAPTER FIFTH. 



REASONING ON FACTS. 



109. A different mode of reasoning from eith- 
er of the preceding is used in the investigation 
of those important and interesting truths, which 
are comprised under the general name o^ facts. 
These are for the most part so unconnected 
and independent, so transient in their exist- 
ence, and so dissimilar in the causes, which 
produce, and the circumstances, which attend 
them, that they cannot be deduced from any 
general principles of reasoning. The proofs, 
by which alone they can be estabhshed, must be 
derived from impressions, made on the senses 

* Locke, Essay on the Understanding, b. iv. ch. 16. CampbclF, 
Phil. Rhet. vol. i. b. i. ch. 5. sect. 2. Beattie, Essay on Truth, part k 
ch. 2. sect. 7. Tatham, Chart and Scale of Truth, vol. i. eh. 1, 
sect. 3. Stewart, Elem. Phil. Mind, vol. ii. ch. 4. sect. 4. Gambler, 
Moral Evidence, ch. 2. 



REASONING ON FACTS. 89 

of some persons, to whose immediate observa- 
tion the facts themselves, or some appearances, 
connected with them, must have been present- 
ed. The truthsj belonging to this class, form 
the largest and most valuable part of our 
knowledge. They enter into the business of 
human life ; and deeply involve the happiness 
both of individuals and of communities. 

110. Facts may be distinguished into three 
classes, in reference to the evidence, by which 
they are judged. Some are admitted on tes- 
timony alone ; some on circumstantial evidence 
alone ; and some on these two united. 

First, human testimony is the evidence, on 
which we place most reliance for our knowledge 
of such facts as have not fallen under our im- 
mediate observation. We readily admit the 
reality of a fact on the sober declaration of a 
person, whose veracity we have no positive 
reason for distrusting. Truth is naturally 
agreeable to the human mind ; for people 
usually speak as they think. No effort of 
invention is required to relate things as they 
are ; but arts of deception require study ; and 
are seldom practised, but for criminal purposes. 
The moral sense is rarely, if ever, depraved 
8^ 



90 REASONING ON FACTS. 

to such a degree, as to lose all preference of 
truth to falsehood. 

111. A propensity to believe what others 
assert has also its foundation in the constitution 
of the mind, in the same manner as the ten- 
dency to veracity. Children at first believe 
every thing that is told them ; which is a wise 
provision, as testimony is to them the princi- 
pal means of obtaining knowledge. This dis- 
position to unlimited credulity continues, till 
experience begets distrust, and at length teach- 
es the necessity of restraining our confidence 
in testimony within certain limits. 

112. Testimony is either oral or written. 
Oral testimony is distinguished into original j 
and transmitted or traditional. It is original 
when it is derived from one^ who had sensible 
evidence of the fact asserted. This is the only 
testimony of this kind, in which we can have 
full confidence ; and, when accompanied by 
circumstances of the most favourable nature, 
produces a firm behef ; even though it be the 
declaration of a single witness. 

113. When several independent original 
witnesses, w^ith equal advantages for knowing 
the fact, which they assert, and without any 



REASONIING ON FACTS. 91 

previous concert, agree in their report, they 
mutually strengthen each other's testimony. 
This concurrence of several independent testi- 
monies is itself a probability, distinct from 
that, which may be termed the sum of the 
probabilities, resulting from "the separate testi- 
monies of the witnesses ; a probability, which 
would remain, even though the witnesses were 
of such a character as to merit no confidence. 
That such a concurrence should be accidental 
is in the highest degree improbable. If, there- 
fore, concert be excluded, there remains no 
other cause for the concurrence, than the ex- 
istence of the fact. 

114. That evidence, which is professedly 
given on a certain subject, is called direct tes- 
timony. But a declaration, uttered in famil- 
iar conversation, or casually made in the 
course of a speech or discourse, may be appjed 
as evidence on a subject in no way connected 
with that, on which it was originally introduc- 
ed. This is termed incidental testimony, and 
it is usually considered of greater validity than 
that, which is direct ; because, from the manner 
in which it was introduced, there is less reason 



92 REASONING ON FACTS. 

to apprehend any deliberate intention to de- 
ceive. 

115. When a witness asserts a fact, which 
he did not personally observe, but which he 
received from the mouth of some other person, 
his testimony is called transmitted or tradition- 
al. The general principle with regard to this 
sort of testimony is, that the further it travels 
from its original source, that is, from the im- 
mediate witness of the fact, the weaker it be- 
comes. The existence of a fact, reported by 
several persons in succession, becomes a prob- 
ability, resulting from a series of probabiUties, 
successively founded on each other. Each per- 
son can affirm no more than what he received 
from his immediate informant, and the channel, 
through vv^hich the report was said to have 
passed from the original witness to him. 

116. The circumstances, constituting what is 
called the credibility of a witness, are the follow- 
ing : First, sufficient discernment^ opportunity^ 
and attention^ to obtain a clear knowledge of 
the fact attested. Secondly, disinterestedness^ 
which, in its full extent, implies the absence of 
all expectation of advantage or detriment, aris- 
ing from the testimony, either to the witness 



REASONING ON FACTS. 93 

himself, or to his friends, sect, or party. 
Thirdly, integrity. This affords the strongest 
assurance of a true testimony, inasmuch as it 
is absolutely inconsistent with any intention to 
deceive or prevaricate, as well as with a con- 
scious ignorance of the fact attested. To 
these may be added the sanction of an oath, 
with a knowledge of its nature and of the high 
penalties annexed to perjury. But testimony 
under oath is principally confined to juridical 
proceedings. It is rarely employed in settling 
historical facts, or the ordinary events of 
human life. So far as a witness is deficient 
in either of the above qualifications, so far 
will this deficiency invalidate his testimony. 

117. Written testimony is usually esteemed 
stronger, and more deserving of confidence, 
than oral ; for the record, being made, for the 
most part, without a knowledge of the uses, to 
which it is afterwards applied, may be presum- 
ed to have been made without any undue bias : 
and the witness has more time to contemplate 
the fact, and wxigh the circumstances, so as to 
render his account accurate. Further, as the 
record of facts is usually made soon after they 
occur, this testimony is secure against any 



94 REASONING ON FACTS. 

suspicions, arising from the imperfection of 
memory, which often weakens the force of oral 
testimony, especially on subjects of a distant 
date, where circumstances are liable to be 
forgotten, and conjectures substituted in their 
stead. 

118. Written testimony is also less hable to 
have its credibility impaired by transmission 
than oral. For, as the original record is com- 
monly preserved for many years, it may be 
compared with the successive copies, and the 
slightest disagreement may easily be detected. 
Whereas oral testimony is fugitive in its na- 
ture, and the existence of the original witness 
must be determined by the testimony of a sec- 
ond witness, whose existence must be admitted, 
in like manner, on the credibility of a third, 
and so on. Besides, the care, which copying 
requires, gives a copy a preference to transmit- 
ted oral testimony. Mistake, in the former, is 
much less likely to be committed. 

119. If several independent copies be taken 
of an original record, and these agree in all 
material circumstances, their credibility, with 
respect to the object testified, is nearly equal 
to that of the original record. For it is highly 



REASONING ON FACTS. 95 

probable, that the different copies would sub- 
stantially agree ; and scarcely possible, that 
the same error should be committed in all. The 
same remark is applicable to all the successive 
copies, and the more numerous they are, the 
more they strengthen each other. 

120. In all plural testimony, whether oral 
or written, the several witnesses are required 
to agree in every important circumstance. 
But in things of minor consequence, a certain 
degree of discrepancy tends rather to increase, 
than to diminish, the credibility of the testi- 
mony ; for such a discrepancy is what must 
naturally be expected from different persons, 
describing the same things. 

121. General notoriety is a ground of behef, 
extending both to specifick facts and general 
truths. It IS a species of testimony differ- 
ent from either of the preceding in this, that 
the information is not derived, i7nmediately or 
remotely^ from any one, who pretends to have 
personally witnessed the fact, or investigated 
the truth in question. No person can examine 
every subject for himself, so as to have full 
knowledge of the truth of every proposition, 
which he finds it necessary to believe. Many 



96 REASONING ON FACTS. 

things must be received on trust. Most men 
can give no better reason for their beUef of 
the greater part of the facts and general truths, 
which they receive, than that they find them 
universally believed by others. 

122- The weight of this evidence depends 
partly on the presumption, that, unless the 
assertions were true, their falsehood would 
have been detected ; and partly on experience ; 
for, though we are in the constant practice of 
admitting them as unquestionable truths, we 
rarely find ourselves deceived. 

123. This species of evidence should not be 
applied without discrimination. Mathematical 
subjects admit of being certainly known, and 
mistakes respecting them may be easily cor- 
rected. In these, therefore, propositions uni- 
versally believed may be "elied on with safety. 
The same may be observed of all assertions 
concerning the existence and qualities of ma- 
terial things ; and also concerning those facts 
and events, which are subject to the observa- 
tion of many persons. But the case is diflfer- 
ent with respect to those propositions, which, 
if false, could not be easily disproved ; such, 
for example, as relate to events, which could 



EEASONING ON FACTS^ 97 

have been observed only by a few persons ; or 
to things, supposed to have happened in re- 
mote antiquity, or in fabulous ages. Genercd 
notoriety or universal belief, with regard to 
such propositions, is not a sufficient ground of 
assent. 

124. Secondly, there are many events and 
occurrences, which, as they happen not within 
the notice of any one, can be judged of only 
by a train of circumstances ; and this evidence 
often produces a higher degree of assurance, 
than the testimony of living witnesses. Cir- 
cumstances can neither falsify nor withhold 
the truth ; and an event is considered as well 
established, when a number of these are of 
such a nature, that they cannot be satisfactorily 
accounted for in any way, but by admitting 
the event in question. 

125. Belief, grounded on circumstantial evi- 
dence, is usually denominated presumption ; 
and presumptions are either slight or violent, 
according as the circumstances noticed are 
more or less necessary to the fact supposed, or 
do more or less usually and exclusively attend it. 
Thus, the presumption, that a person is the 
author of an essay, barely because the hand- 

9 



98 REASONING ON FACTS. 

writing resembles his, is only slight ; for one 
person may imitate the hand of another, and 
two persons may resemble each other in their 
usual manner of writing. But, to render the 
presumption violent, the circumstance must be 
such, not only as would necessarily have at- 
tended the fact, had it existed, but such as 
could not be supposed to have existed ; unless 
the fact in contemplation had existed likewise. 
Thus, a cottage, discovered on a desolate 
island, affords a violent presumption, that some 
human being had been there before. A shel- 
ter of some kind would be a natural, if not a 
necessary consequence of a person's having 
resided there ; and there is no other way, by 
which the existence of the cottage can be 
accounted for. 

The fact, on which a presumption is ground- 
ed, must be clearly proved ; for a presumption 
cannot be raised on a mere conjecture. 

126. Thirdly, the credibility of attested facts 
may be heightened by the analogy of those 
facts to our general experience in similar cases, 
or to what reason would lead us to expect. 
This analogy is denominated internal evidence. 
Facts, which are rendered probable by inter- 



REASONING ON FACTS. 99 

nal evidence, may have their probability in- 
creased by testimony, though in different de- 
grees. If an asserted fact agree w^ith our con- 
stant and invariable experience, its probability 
can be but little augmented by the most unex- 
ceptionable testimony. Thus, the freezing of 
w^ater is so common in our climate, that, should 
any person affirm, that Charles river was frozen 
over in February, fifty years ago, we could 
have no hesitancy in believing it. Nor would 
our assurance of the fact be increased, by the 
united testimony of five hundred witnesses, of 
the most undoubted veracity. 

127. Where the internal probability is less, 
more testimony is required to produce belief; 
as, if it were asserted, that there was thunder 
in May, or frost in October, in any particular 
year. These events, happening not uniformly, 
though much oftener than they fail, receive but 
a shght confirmation from past experience. 

128. Those facts, which are called indiffer- 
ent or equicasual^ by reason of the irregularity 
of their appearance, belong exclusively to the 
province of testimony ; as, whether a ship sailed 
on Tuesday or on Friday ; whether a man made 
his will, or died intestate. The probability, 



100 REASONING ON FACTS. 

that any asserted fact of this sort happened at 
any specified time or place, will be just equal 
to the credibility of the witnesses attesting it. 

129. If the asserted fact be of an extraordi- 
nary nature, and one, that militates with our 
general experience in similar cases, it will be 
assented to with difficulty ; as, if it were as- 
serted, that there was sno\Y in August, or that 
the same number drew the highest prize in five 
successive lotteries. The internal improbabil- 
ity of such facts must be overcome by an in- 

i creased weight of testimony. 

130. Those facts or events, which are admit- 
ted with the greatest difficulty of all, are such 
as are supernatural^ or miraculous. These^ 
contradicting our invariable experience, and 
opppsing the well known laws of corporeal 
nature, are in themselves in the highest degree 
improbable ; and require for their belief a 
testimony so ample, and attended by such 
circumstances, as would render its falsehood 
no less miraculous than the fact attested.^ 

* Gilbert, Law of Evidence. Kirwan, Logick, part iii. ch. 6. 
Locke, Essay on the Understanding, b. iv ch. 16. Gambier, Mora] 
Evidence ch. 2. 



CALCULATION OF CHANCES. 101 

CHAPTER SIXTH. 

CALCULATION OF CHANCES. 

13L By chance is not meant the negation of 
a cause, but our ignorance of it. Every change 
in the universe must proceed from some ade- 
quate cause. When we speak of events as 
happening fortuitously^ or by chance^ we mean 
no more, than that the causes, which produce 
them, are wholly unknown to us. The bare 
possibility of an event is often denominated a 
chance ; and where there are several known 
causes equally capable of producing different 
events, it is manifest, that there are so many 
chances of those events ; and that no one of 
them is more probable than the rest. 

132. The doctrine of chances is thatj which 
teaches the degree of probability or improbabiU 
ity of any one of a given number of events^ con- 
sidered as equally possible. Thus, on throwing 
a die, it is certain that some one of its six faces 
will be turned up ; but, as only one of these six 
faces can present an ace, the chance of throw- 
ing an ace is only one out of six chances, or i; 
and the chances against it are five out of six, 
or f of 9 certainty. Hence the general rule 
9^ 



102 CALCULATION Oi^ CHANCES. 

ia, that the probability or improbability of any 
event is, as the number of the favourable chances^ 
divided by the sum of all the chances, both fa- 
vourable and unfavourable. 

133. The degree of probabiUty, that any 
event will or will not happen, is conveniently 
expressed by a fraction, whose numerator rep- 
resents the number of chances, which favour 
the existence, or the nonexistence of the event ; 
and whose denominator is the sum of all the 
chances, both favourable and adverse to the 
event. Thus, if an event have five chances to 
happen and three to fail, the fraction I w^U ex- 
press the probability of its happening, and the 
fraction f, that of its failure. These t\\^ frac- 
tions, which represent all the chances, both of 
happening and failing, being added together, 
their sum will always be equal to unity ; since 
the sum of their numerators will be just equal 
to their common denominator. And as in 
every case it is certain, that an event will 
either happen or fail, it follows, that certainty 
is justly represented by unity. 

134. The expectation of obtaining a benefit, 
which depends on the happening of an uncer- 
tain event, has a determinate vahie before the 



CALCULATION OF CHANCES. 103 

event takes place. The value of this expepta- 
tion is in all cases estimated by multiplying the 
value of the benefit expected by the fraction, 
"vvhich represents the probability of obtaining it. 
Thus, if 60 crowns be promised a person on 
condition of his throwing a particular face on 
a die, his expectation before trial is worth 10 
crowns, since he has one chance in six, or i of 
a certainty of gaining the whole sum. 

135. Events are either independent o^ de- 
pendent. Tivo events are independent^ when 
they have no connexion ivith each other ^ and the 
happening of one neither promotes nor hinders 
the happening of the other. Thus, throwing 
an ace on one die affects not the possibility of 
throwing it again on the same, or on another 
die. But the possibility of ^ joint event on two 
dice, though each is independent of the other, 
singly considered, is affected by all the possibil- 
ities of failure in each of the conjoined events. 
Now there are thirty-six possible events on 
two dice considered conjointly ; for each has 
six faces, and each face of the one may be com- 
bined with each face of the other. Therefore 
the possible appearances are 6 X 6 = 36. But, 
of these combinations, there is but one pro- 



104 CALCULATION OF CHANCES. 

ductive of the appearance of two aces, or any 
other two faces. So that the chance of throw- 
ing two aces either together on two dice, or 
successively on one die, is only sV. 

136. Hence the probabihty of two or more 
independent but joint events is equal to the 
product of the chances of each. Thus, the 
probability of throwing three aces successively 
on one die is i X i X i = ^ie. So if the proba- 
bility, that one man. A, will live a year, be ^, 
and the probability of the hfe of another man, 
B, for one year, be td^, the probability, that 
both will live another year, is but -r^ X ^ = 
T^^. Hence the concurrence of two events is 
less probable than the occurrence of either ; 
and is even improbable, though each is prob- 
able and completely independent of the other. 

137. From the foregoing rule it is manifest, 
that the jomt occurrence of two or more equi- 
casual, independent events is improbable ; and 
the more so, the more numerous they are. For 
the probability of each is i ; therefore the joint 
chance of two such events is i X i = i; and of 
three such events is i X i X i=i. So the con- 
currence of two independent, improbable facts 
is still more improbable. For, supposing the 



CALCULATION OF CHANCES. 105 

improbability of one of them to be i, and that 
of the other i, their joint improbabihty would 
be sV. By the same rule, the improbability 
of the death of A within a year being t^. and 
that of the death of B within a year t^, the im- 
probability, that both will die within a year, 
is Tu X 1^ = TOT. And the probability that one 
of the events will happen and the other fail is, 
as the probability of the happening of the one, 
multiplied by the probability of the failure of 
the other. So, in the above case, the prob- 
ability, that A will live and that B will die, 
is A X T^ = 1^. And the probability, that 
B will live and that A will die, is A X t\ = 

138. A dependent event is one^ whose exist- 
ence is rendered more or less probable by the 
chances attending the existence of another event. 
When several events are connected in such a 
manner, that the second depends on the first, 
the third on the second, and so on, the prob- 
ability of the first or independent event must 
be first ascertained ; that of the second, which 
depends on the first, is then found, by mul- 
tiplying its separate probability into that of 
the first; and the product will give the real 



106 CALCULATIOIN OF CHANCES. 

probability of the second event. In the same 
manner we proceed to find the probabiHty of 
a third or fourth dependent event. 

139. Thus, suppose six white and six black 
balls to be placed in a box, and through a hole 
in the box, two balls to be successively draw^n 
out ; and let it be required to determine the 
probability, that both these v/ill be white. As 
there are twelve balls in the box, and six of 
them are white, it is evident, that the proba- 
bility of drawing a white ball at the first trial 
will be tV But the chance of doing this on 
the second trial will be diflTerent ; for, as one 
of the balls has been taken out, there are but 
eleven remaining ; and since, in order to the 
second trial, it is necessary to suppose, that the 
ball removed was a white one, the remaining 
number of these is reduced to five. The sep- 
arate probability, therefore, of drawing a white 
ball at the second trial will be only A ; and 
the chance of drawing it the first and second 
time will he r^ = i X ^ = ^^. The separate 
probability of drawing out a white ball at a 
third trial, since two white balls have been 
removed, will be -h ; and the chance of draw- 
ing three white ones, at three successive trials 
will be i X A X ^ = ^ = tV. 



CALCULATION OF CHANCES. 107 

140. Again, W sailed for Africa in a fleet 
of twelve ships, three of which were lost in a 
storm, on the first part of the voyage. Of the 
crews of the nine ships, that escaped the storm, 
one third part perished from the hardships, 
they met on the voyage. We wish to ascertain 
the probability, that W has escaped both 
calamities. Now, as the chance of his having 
survived the hardships of the voyage depends 
on the event of his having escaped the storm, 
the probability of the last named event must be 
first ascertained. If this be found improbable, 
the second event must fail ; but if it be found 
probable, the second event may exist, and the 
probability of its existence may be found by 
the rule already given. [No. 138.] 

141. As nine ships out of tlie twelve surviv- 
ed the storm, the probability that W escaped 
in one of them is A = f • This being suppos- 
ed, the probabiHty of his having escaped the 
second danger, since only one third of those, 
who survived the storm, perished, is f • Hence 
the probability of his having lived through 
both dangers is f X f = y^s- = i- Therefore it 
is merely doubtful whether he survived both 
calamities. If only i of the crew survived the 



108 DEMONSTRATIVE REASONING. 

second danger, then his escape would be im- 
probable ; for f X i = 1^. If only two out of 
the twelve ships were lost, and consequently ten 
had escaped the first danger, and I of the crew 
had escaped the second danger, as above, then 
the probabihty of his entire survival would be 
TfXf = ft = f; a slight probabiUty-* 



CHAPTER SEVENTH. 

GENERAL DESCRIPTION OF DEMONSTRATIVE REASONING. 

142. The general nature of demonstrative 
reasoning has already been explained, in point- 
ing out the circumstances, which distinguish it 
from moral, or probable reasoning. [See No. 
87 to 93.] It has generally been admitted, 
that demonstration can be employed only about 
such truths as have been termed necessary^ the 
subjects of which are not supposed to have any 
real existence, but to be abstractly conceived 
by the mind. All created beings depend on 
the will of their Creator. Their existence, 
their properties, and of course the relations, 
subsisting among those properties, are contin- 

* Demoivre, Doctrine of Chances, Introduction. Kirwan, Logick. 
part iii. oh. 7. 



-DEMONSTRATIVE REASONING. 109 

gent, and perpetually varying- Gur reasoning 
on these must be grounded on the observation 
of our senses ; and the conclusions, which 
we make, are liable to be uncertain. But 
demonstrative reasoning, being grounded on 
exact and adequate definitions, and proceed- 
ing by the successive application of general 
propositions, which have an intuitive agree- 
ment with each other, affords satisfaction in 
every step ; and the mind advances to the 
conclusion with the fullest assurance of cer- 
tainty. 

143. Demonstration is best adapted to the 
exact sciences of number and quantity. Arith- 
metick and geometry possess many important 
advantages with respect to this method of rea- 
soning. Their terms are free from all ambi- 
guity. Their first principles are simple -and 
obvious. The subjects, about which they are 
conversant, are wholly independent of things 
in actual existence, and capable of being per- 
fectly defined. The properties, belonging to 
these subjects, and their various relations, are 
necessary and immutable. These circumstan- 
ces impart to mathematical demonstrations a 
clearness and force, which cannot be obtained 
10 



110 DEMONSTRATIVE REASONING. 

in Other sciences. For these reasons many 
have maintained, that demonstrative reason- 
ing can be used only within the precincts of 
mathematicks. Many others have controvert- 
ed this position ; and have contended, that 
this method may, at least occasionally, be 
employed in other sciences. 

IM. Mr. Locke advanced the opinion, that 
moral subjects are as susceptible of demonstra- 
tion as mathematical. His reason for this 
opinion is thus stated in his Essay on the 
Understanding :* '' The precise, real essence 
''of the things, moral words stand for, may 
*' be perfectly known ; and so the congruity or 
" incongruity of the things themselves be cer- 
" tainly discovered ; in which consists perfect 
'' knowledge.'' He adds, " definition is the 
"only way whereby the precise meaning of 
'' moral words can be known ; and yet a way, 
" whereby their meaning may be known cer- 
'^ tainly^ and without leaving any room for 
" contest.'' In another placet he says, " the 
''relation of other modes may certainly be 
" perceived, as well as those of number and 

* Book iii. ch. 11. sect. 16. 
t Book iv. ch. 3. sect. 18. 



DEMONSTRATIVE REASONING. Ill 

" extension ; and I cannot see why they should 
" not also be capable of demonstration, if due 
" methods were thought on to examine or pur- 
" sue their agreement or disagreement." 

145. Dr. Reid distinguishes demonstrative 
reasoning into two kinds, which are metaphy- 
sical and mathematical. ''In metaphysical 
" reasoning," he observes, " the process is 
'' always short. The conclusion is but a step 
'' or two, seldom more, from the first principle 
'' or axiom, on which it is grounded ; and the 
" different conclusions depend not one upon 
" another. It is otherwise in mathematical 
'' reasoning. Here the field has no limits. One 
''proposition leads to another; that to a third, 
" and so on without end. If it should be asked, 
" why demonstrative reasoning has so wide 
"a field in mathematicks, while, in other 
" abstract subjects, it is confined within very 
" narrow limits ; I conceive this chiefly owing 
" to the nature of quantity, the object of math- 
" ematicks."^ 

146. Demonstration, in the customary sense 
of the term, appears not to be absolutely cir- 
cumscribed by the narrow limits of a single 

* Essays on the Intellectual Powers, essay vii. ch. 1. 



112 DEMONSTRATIVE REASONING, 

science. Wherever the subjects of our reason- 
ing are independent on the existence of things, 
and are of a nature to afford exact definitions 
and general propositions of undoubted certain- 
ty, there this method of reasoning may be 
employed. And it appears unnecessary to 
concede, that these elements of demonstration 
are no where to be found, except in the sci- 
ence of mathematicks. 

147. Professor Scott, speaking of Dr. Reid's 
division of demonstrative reasoning, says; '' It 
" evidently cannot be meant by Dr. Reid, that 
'' metaphysicks is a science demonstrable in all 
" its parts, like mathematicks. He was too 
•^^ well acquainted v^rith the general uncertainty 
'^ of metaphysical speculations to have ad vane- 
" ed such an opinion. If then he asserts only^ 
'' that several metaphysical truths admit of 
" demonstration, the same ought doubtless to 
"be said of phy&icks, many of the reasonings 
" of which have at least as much of demonstra- 
" tive certainty as any of the speculations of 
"metaphysicks. The truth appears to be, 
" that every branch of science may occasional- 
" ly assume the demonstrative form. The ex^ 
" istence of a Deity, the immateriality of the 



DISTINCTIONS OF REASONING. 113 

*' human soul, and other moral or metaphysical 
" truths, have perhaps been as fairly demon- 
" strated as the Pythagorean proposition, or 
'' the parabolick motion of projectiles. But 
" some sciences are much more susceptible of 
" this kind of proof than others ; physicks 
" admitting much more of demonstration than 
" metaphysicks, or morals. Of all the sciences, 
'' mathematicks is that, which admits the most 
" largely of demonstration. Its first principles 
" are so certain, so definite, and clear ; and its 
"manner of proof so accurate and legitimate, 
" that it may fairly be called a completely de- 
" monstrative science, and the only one, which 
" is justly entitled to that name.''^ 



CHAPTER EIGHTH. 

DISTINCTIONS OF REASONING. 

148. Reasoning is further distinguished 
into that, which is a priori^ and that, which is 
a posteriori. Reasoning a priori is that^ which 
deduces consequences from definitions formed^ 
or principles assumed ; or which infers effect:^ 
from causes previously known. The books of 

* Elem. of Intell. Phil. chap. 8. sect. 4. 

10* 



ir4 DISTINCTIONS OF REASONING; 

matliematicks afford numerous instances of 
conclusions legitimately drawn from definitions 
and assumed principksr We also reason a 
priori whenever we judge of effects from a 
knowledge of the causes^ which produce them. 
Thus we infer, that an eclipse of the sun and 
an eclipse of the moon can never happen 
within twelve days of each other, from our 
knowledge of the causes^ which occasion those 
phenomena. 

149. Reasoning a posteriori is the reverse of 
the former process. By this we deduce causes 
from effects. Thus we infer, that the earth is 
spherical from its shadow on the moon in a 
lunar eclipse ; and we infer the being of a God 
from our own existence and that of the objects 
around us. All reasoning concerning the 
properties and laws, both of mind and body, 
proceeds on this principle. It is only by a 
careful observation of facts, that the laws, 
v/hich regulate them, can be discovered. 

150. Another distinction of reasoning is 
into direct vcnA indirect. The reasoning is di- 
rect^ when the proofs are so applied^ as to show 
immediately the agreement or repugnancy between 
the subject and predicate of the proposition in 



DISTmCTlONS OF REASONING* IT5 

question. In indirect reasoning,^ the argu- 
ments, which we employ, are not intended pn- 
marily to show the relation between the terms 
of the proposition, whose truth we would 
establish ; but to prove the falsehood or absurd- 
ity of the proposition, to which it is opposed. 
This method may be adopted, whenever it is 
manifest, that the proposition, which we allege, 
or its contrary, must be true. We may then 
prove the impossibility of the contrary propo- 
sition ; or we may show^ that a manifest ab- 
surdity must follow from admitting it ; and 
in either case we establish the truth of our 
original proposition. The former course is 
usually called a proof per impossibile ; and the 
latter, a reductio ad absurdum. 

151. Mathematicians make frequent use of 
indirect reasoning. Thus, Euclid proves, by 
an indirect course, that, " if two circles touch 
" each other internally, they cannot hav^e the 
" same centre." He first supposes the contra- 
ry to be true, namely, that the two circles have 
the same centre ; and no third supposition can 
be made ; for they must either both have the 
same centre or not. He then demonstrates the 
impossibility of the case assumed ; and thence 



116 SYLLOGISTICK REASONING. 

infers the truth of the proposition, which he 
first asserted. So moralists prove the exist- 
ence of an all-wise and powerful Creator, by 
tracing the absurdities, which the contrary 
supposition involves. 

152. Another form of indirect reasoning, in 
frequent use, is denominated reasoning a forti- 
ori. This consists in deducing a proposition, 
as true, from less obvious propositions, embrac- 
ed by the same general principles. Thus, if 
the felon, who robs on the highway, deserves 
the punishment of death, this retribution is due 
a fortiori to the wretch, who has committed 
parricide. 



CHAPTER NINTH. 

GENERAL DESCRIPTION OF SYLLOGISTICK REASONING. 

153. All reasoning proceeds by comparison ; 
and two comparisons are necessary to enable 
us to make a conclusion. The subject and 
predicate of the proposition to be proved must 
be separately compared with some third term, 
or common measure ; and from these compari- 
sons we infer their agreement or repugnancy^ 



SYLLOGISTICK REASONING. IIT 

This process, when expressed in words, con- 
sists of three propositions, and has been termed 
syllogism.^ 

154. Syllogism was regarded, for many cen- 
turies, as the only sure instrument of reasoning ; 
and skill m the use of it as the highest ac- 
complishment, which the mind can possess. It 
derived its celebrity from^ the talents and in- 
dustry of Aristotle, who traced and analyzed its 
principles, subjected it to laws, and exhibited 
it in all the variety of modes tmdjiguresj into 
which it could be moulded. Since the time 
of that philosopher, the name s^yllogism has 
usually been employed to denote an argument, 
framed according to certain technical rules of 
art. But it is sometimes used in a larger sense, 
to imply any process of reasoning from more 
general to less general, in opposition to the 
principle ofanaly tical induction. In this sense, 
it will apply to mathematical reasoning; for 
all demonstrations in this science proceed on 
this fundamental principle of the syllogism, 
that whatever may he affirmed of any genus 
may be affirmed of all the species included un- 
der it. 



/ 



118 SYLLOGISTICK REASOiSING. 

155. Syllogism and induction proceed in 
opposite directions. Induction, as has already 
been observed, begins with individual objects, 
as they exist in nature, and ascends by succes- 
sive steps to the most general truths. Syllo- 
gism begins where induction terminates. It 
commences with some universal proposition, 
and follows back the footsteps of the former 
process, transferring at each stage the predi- 
cate of the more general to the less general 
rank of beings ; or, in other words, predicating 
the genus of the species, and the species of 
the individual. 

156. The difference ot these methods may 
be shown by the following example. We ob- 
serve that the individual people of our acquaint- 
ance are constantly dying around us ; that men 
rarely live to the age of a hundred years, and 
that the former generations are wholly swept 
from the earth. From these facts we infer, 
that death is the common lot of our species. 
Observing also, that the same fatality attends 
the various species of beasts, birds, and insects, 
we deduce the more general conclusion, that all 
animals are mortal. This inductive process, re- 
versed in syllogistick language, would run thus. 



SYLLOGISTICK REASONING. ll9 

AH animals are mortal ; 
All men are animals ; 
Therefore all men are mortal. 

All men are mortal ; 
W. X. Y. are men j 
Therefore W. X. Y. are mortal. 

157. Syllogism is employed with advantage 
in communicating to others, in an exact and 
perspicuous manner, the general principles of 
science. It may also be used with success in 
exposing the weakness of arguments, stated in 
loose or figurative language. But it is of no 
service in helping us to the discovery of new 
truths. We must know a thing first, Mr. 
Locke observes,^ and then we can prove it 
syllogistically. 

168. As syllogism operates wholly on gen- 
eral propositions, and definitions previously 
established, the justness of its conclusions must 
depend ultimately on the accuracy, with which 
the inductive processes have been conducted. 
•• The syllogism," says Lord Bacon, " is form- 
•^'ed of propositions ; propositions, of words ; 
-' and words are the marks of ideas. If there- 
" fore ideas themselves, which make the ground- 
'•work of our reasonings, are confused, and 

* Essay, b. iv, ch. 17. 



120 REGULAR SYLLOGIS^MS. 

" formed from a hasty observation of things, 
" the conclusions, which we make from them, 
^'will be without soUdity. The whole there- 
^' fore depends on the accuracy of our induc- 
^'tions-''* 



CHAPTER TENTH. 

OF REGULAR SYLLOGISMS. 

159. The most general division of syllogisms 
IS into single and compound. Of single syllo- 
gisms, some are regular and some are irregular. 
A regular syllogism is an argument^ consisting 
of three propositions^ the last of which is deduced 
from the two preceding^ and is substantially con- 
tained in them. Example : 

Every human virtue should be habitually practised ; 
Industry and temperance are human virtues ; 
Therefore industry and temperance should be habitually 
practised. 

160. This is a concise and luminous method 
of evincing the agreement or repugnancy be- 
tween the subject and predicate of a proposi- 

* ^^ Syllogismiis "ex propositionibus constat } propositiones, ex 
*^ verbis ) verba notionum tesserae sunt. Itaque si notiones ipsa?, 
" id quod basis rei est, confusas sint, et temere a rebus abstractas, 
" nihil in iis, quas superstruuntur, est firmitudinis. Itaque spes est 
'* una in inductione verd," JVovum Organum, lib. i. aph. 14. 



REGULAR SYLLOGISMS, 121 

tion. A third term, having a common relation 
to them both, is invented, and applied to them 
successively, in two distinct propositions. 
These are called premises^ because from them 
the proposed question is inferred, as a conclu- 
sion ; and its subject and predicate are either 
joined or separated, according as they were 
found m the premises to agree, or not, with 
the term introduced. It is obvious, that, if 
any tivo things agree with a third, they must 
agree with each other ; and that tivo things, of 
which one agrees, and the other disagrees, with 
a third, must disagree with each other. The 
former of these rules is the foundation of all 
affirmative conclusions, and the latter of all 
negative. 

161. The names of the three propositions 
are the major^ the minor, and the conclusion. 
These are composed of three terms, denomin- 
ated the major, the minor, and the middle terms. 
The predicate of the conclusion is called the ma- 
jor term,^ because it is the most general ; and 
the subject of the conclusion the minor term, 
because it is the least general. These two are 
also denominated the extremes ; and the third 

* See note B, at the end of the book. 

11 



122 REGULAR SYLLOGISMS. 

term^ introduced as a common measure be- 
tween them, is called the mean or middle term^ 
because its extension is less than that of the 
major, and greater than that of the minor term. 
[See No. 35.] This circumstance proves the 
natural situation of the middle term to be that 
of subject in the major premise, and of predi- 
cate in the minor ; since the predicate of a 
proposition is never less, but usually more 
general, than the subject. 

162. In forming the syllogism, each term is 
taken twice, and no more. The middle and 
major terms constitute the major premise ; the 
minor and middle terms the minor premise ; and 
the two extremes^ connected by a copula^ make 
up the conclusion. The major proposition 
must always be universal, but may be either 
affirmative or negative ; and the minor prop- 
osition must always be affirmative, but may 
be either universal or particular.* The con- 
clusion may be either universal affirmative, 
universal negative, particular affirmative, or 
particular negative. 

163. In every regular syllogism, the major 
proposition is placed first ; the minor next ; 

* See note C, at the end of the book. 



REGULAR SYLLOGISMS. 123 

and the conclusion last ; as in the following 
example. 

Every vegetable is combustible ; 
Every tree is a vegetable ; 
Therefore every tree is combustible. 

Comhustihle is the major term ; every tree the 
minor term ; and these extremes are joined in 
the conclusion. Vegetable is the middle term ; 
it is subjected in the major premise, and pre- 
dicated in the minor. The major premise must 
always be sufficiently general to involve the 
conclusion ; and must be assumed as a truth 
already known. It cannot be proved by syllo- 
gism. This instrument teaches only how to 
make a legitimate inference of one proposition 
from another. 

164. The truth, proved by the preceding 
example, is, that trees are combustible. The 
major premise, namely, every vegetable is com- 
bustible, is first assumed on the ground of ex- 
perience and observation. The minor premise 
barely asserts the fact, that trees belong to the 
class of vegetables. Now if it be certain, that 
combustion belongs universally to vegetables, 
and that trees are included in that class of 
things, it must of necessity follow, that every 



124 REGULAR SYLLOGISMS. 

tree is combustible ; for it is a primary law of 
syllogistick reasoning, that whatever may he 
affirmed of any general term^ may he affirmed 
of every species and individual included ivithin 
its extension, 

155. In the regular syllogism, each step of 
the reasoning process is distinctly expressed ; 
but, in familiar language, one part is frequent- 
ly omitted, which may be readily found by 
examining the grounds, on which the judgment 
is formed. Thus, 

No language is perfect ; 

Because it is a human invention. 
Perfection is here denied of language, for no 
other assigned reason, than because it is a 
human invention. But there is a latent prop- 
osition, which is the real ground of the judg- 
ment, and must therefore have been distinctly 
contemplated by the mind, namely, no human 
invention is perfect. Let this proposition be 
subjoined to the other two, and the argument 

will stand thus ; 

No language is perfect ; 
Because it is a human invention ; 
And no human invention is perfect. 

This is the regular syllogism reversed ; which, 
rectified, will stand thus ; 



REGULAR SYLLOGISMS. 125 

No human invention is perfect ; 
Every language is a human invention ; 
Therefore no language is perfect. 

166. Every assertion, accompanied by a 
reason why it is made, contains the elements 
of a syllogism, namely, the major, minor, and 
middle terms. Every such assertion, made in 
the familiar form of language, may be trans- 
ferred to a regular syllogism, by observing the 
follow^ing rule : First, distinguish the reason, 
on which the attribute of the given proposition 
is affirmed or denied of its subject, and this 
will be the middle term of the syllogism. Let 
this be taken, in its most enlarged sense, for 
the subject of a proposition, to which, for a 
predicate, unite the attribute of the asserted 
proposition, and the major premise will be 
formed. Next, to form the minor premise, we 
have only to predicate the middle term, already 
found, of the subject of the asserted proposition. 
The original proposition, without the reason, 
before annexed to it, will constitute the con- 
clusion of the syllogism. 

167. For example. Dr. Johnson says of en- 
vy, " It is, above all other vices, inconsistent 
« with the character of a social being, because 

11* 



126 REGULAR SYLLOGISMS* 

" it sacrifices truth and kindness to very weak 
^' temptations.'^ Sacrifices truth and kindness to 
very iveak temptations is the reason, why envy 
is pronounced, above all other vices, inconsist- 
ent with the character of a social being. This, 
then, must form the middle term of the syllo- 
gism. But as this collection of words repre- 
sents an attribute, and not a person or thing 
really existing, it cannot be enlarged, so as to 
become the subject of a general proposition, by 
simply placing before it one of the common 
signs of universality, a//, every^ or each ; it 
must be preceded by some universal sign of 
a different sort, as whatever , that luhich^ or the 
like. Thus ; 

That which sacrifices truth and kindness to very weak 
temptations is, above all other vices, inconsistent with the 
character of a social being ; 

Envy sacrifices truth and kindness to very weak temp- 
tations ; 

Therefore envy is, above all other vices, inconsistent 
with the character of a social being. 

In this manner may the simple elements of 
reasoning, however obscured, in any instance, 
by rhetorical language, or complicated forms 
of speech, be easily collected, and exhibited in 
a regular syllogism. 



REGULAR SYLLOGISMS. 127 

168.^ As the major proposition of a syllogism 
must always be universal, the middle term, as 
the subject of this proposition, must be taken 
in a universal sense. Every middle term must 
represent either some class of persons or things, 
or else some attribute common to a whole class 
of beings. If the middle term denote persons 
or things, something must be asserted, hypo- 
thetically, in the major proposition, to agree 
with, or to be repugnant to, that whole class of 
beings ; and in this class the minor term must 
be included ; which it is the sole business of 
the minor proposition to affirm. In the conclu- 
sion, we apply to the minor term, separately, 
the same predicate, which was applied to it in 
the major proposition, in connexion with the 
whole class of things, to which it belongs. 

169. If the middle term express an attri- 
bute, it must be asserted in the major propo- 
sition, that, to whatever person or thing the 
attribute, forming the middle term, can be as- 
cribed, the major term may be ascribed also. 
In the minor proposition, the attribute, which 
forms the middle term., is declared applicable 
to the minor term. In the conclusion, the 
agreement or repugnancy, which was before 



128 REGULAR SYLLOGISMS. 

admitted between the middle and major terms, 
must be also admitted between the major and 
minor terms. 

170. Any regular syllogism may be reduced 
to the familiar form of reasoning, by the follow- 
ing rule : First, state the conclusion, omitting 
the illative therefore ; then, subjoin the middle 
term together with the minor, or some pronoun 
as its substitute, preceded by some causal par- 
ticle, as since^for^OY because. For example, 

Every animal, possessing wings and feathers, is a bird ; 
An ostrich is an animal, possessing wings and feathers , 
Therefore an ostrich is a bird. 

This syllogism may be thus expressed in the 
familiar form of reasoning ; 

An ostrich is a bird ; 

Because it has wings and feathers. 

171. Each of the preceding syllogisms con- 
cludes w^ith a universal proposition. The con- 
clusions of the four following examples are of 

different kinds. 

I. 
Whoever disregards the rights of his fellow beings, de- 
serves the detestation of mankind ; 
Tyrants disregard the rights of their fellow beings ; 
Therefore tyrants deserve the detestation of mankind. 



REGULAR SYLLOGISMS. 129 

II. 

They, who subvert the foundations of morality and 

religion, ought not to be respected ; 
Atheists subvert the foundations of morality and religion ; 
Therefore atheists ought not to be respected, 

III. 

Every creature, which can live in more elements than 

one, is amphibious ; 
Some animals can live in more elements than one ; 
Therefore some animals are amphibious. 

lY. 

No person of dissolute habits can be a safe companion ; 
Some persons of improved minds are dissolute in their 

habits ; 
Therefore some persons of improved minds are not safe 

companions. 

The conclusion of the first syllogism is a 
universal affirmative proposition ; that of the 
second, a universal negative ; that of the third, 
a particular affirmative ; and that of the fourth, 
a particular negative. These are all the kinds, 
into v^hich propositions are distinguished, in 
reference to quantity and quality.* 

* Common systems Df Logick. CoUardj Logick, part iv. ch. 4^ 5» 



130 IRREGULAR SYLLOGISMS. 

CHAPTER ELEVENTH. 

ENTIIYMEMES. 

172. Besides the regular, categorical syllo- 
gism, described in the preceding chapter, there 
are some other kinds of single syllogisms, which 
have different degrees of irregularity in their 
construction. Among these may be placed 
the enthymeme^ which is an abridged, or de- 
fective syllogism, consisting of the conclusion 
and only one of the premises ; the other being 
suppressed, as too obvious to need insertion. 
It is of very general use, both in writing and 
conversation. 

173. Which of the premises is omitted in 
any instance may be known, by the following 
rule : If the subject of the conclusion be ex- 
pressed in the given premise^ or proposition^ 
containing the reason^ the major premise is 
omitted ; if the predicate of the conclusion be 
expressed, the minor premise is ivanting. Thus, 

Whatever tends to subvert the civil government should 

be deprecated ; 
Therefore civil dissensions should be deprecated. 

Christianity teaches the way to future happiness ; 
Therefore it should be diligently sought. 



IRREGULAR SYLLOGISMS. 131 

The minor premise is omitted in the first ex- 
ample, and the major in the second. Let these 
be supphed, and the syllogisms will be complete. 

Whatever tends to subvert the civil government should be 

deprecated ; 
Civil dissensions tend to subvert the civil government ; 
Therefore civil dissensions should be deprecated. 

That knowledge, which teaches the way to future happi^ 

ness, should be diligently sought ; 
Christianity teaches the way to future happiness ; 
Therefore Christianity should be diligently sought. 

174. Enthymemes may be expressed in 
various ways, and have sometimes been dis- 
tinguished into several kinds. Those are the 
most regular, which conform to the syllogistick 
order. In these the conclusion is placed after 
the proposition, which contains the proof; and, 
by supplying the omitted proposition, the syl- 
logism is rendered perfect, without any other 
alteration. But, in familiar conversation, it is 
more common to express the conclusion first, 
and then to subjoin the reason, on which it is 
grounded, preceded by a causal particle. As, 

Enthusiasm should be avoided ; 
Because it leads us astray from reason. 



132 IRREGULAR SYLLOGISMS. 

They, who deny a future state of retribution, are in 
error ; 

For they deny the doctrine of the Bible. 

175. Although the conclusion be placed 
after the reasoning proposition, still the enthy- 
meme will not be regular, unless the syllogis- 
tick language and arrangement be employed. 
The following sentence is an enthymeme of 
this sort : 

" Since it is the understanding, that sets man above the 
" rest of sensible beings, and gives him all the ad- 
" vantage and dominion, which he has over them ; 

" It is certainly a subject, even for its nobleness, worth 
" our labour to inquire into,"* 

Each of these enthymemes contains the ele- 
ments of a syllogism, namely, the major, minor, 
and middle terms ; which may be easily dis- 
tinguished. The suppressed propositions are 
readily supplied by the mind ; and the omis- 
sion of them contributes to the brevity and 
elegance of language. 

176. An act of reasoning may be stated 
hypothetically ; thus. 

The African slave-trade should be discountenanced ; 
If it be a violation of the natural rights of man. 

* Locke, Essay, Introduction. 



IRREGULAR SYLLOGISMS. 133 

Here the predicate, discountenanced^ is not 
applied to the African slave-trade absolutely ; 
but only on condition of its being a violation 
of man's natural liberty. Still the reasoning 
is the same, as if it were expressed in this 
absolute form : 

The African slave-trade is a violation of the natural rights 

of man ; 
Therefore it should be discountenanced by alL 

The judgment is formed in the two cases by a 
comparison of precisely the same things* 

177. What are here considered as famihar 
enthymemes have usually been received as 
compound propositions, and have been distrib- 
uted into different species, under the heads of 
causal J discretive^ and conditional. But, that 
they cannot justly be regarded as mere prop- 
ositions of any sort, is evident from this, that 
each example contains two entire propositions. 
[See No. 80.] It is equally manifest, that 
they represent complete acts of reasoning, 
since in each the elements of a perfect syllo 
gism are expressed.* 

* Collard, Logick, part. iv. ch. 6, 

12 



134 IRREGULAR SYLLOGISMS. 

CHAPTER TWELFTH. 

CONDITIONAL AND DISJUNCTIYE SYLLOGISMS. 

178. A conditional or hypothetical syllogism 
is one^ whose major proposition is conditionaL 
Thus, 

If men have vicious propensitieSj they need the restraints 

of government ; 
But men have vicious propensities ; 
Therefore they need the restraints of government. 

The major premise consists of two entire prop- 
ositions, which make an enthymeme. The 
minor premise and the conckision constitute 
another enthymeme, expressing the same mean- 
ing as the other, with only this difference, that 
what is stated hypothetically in the first is 
expressed absolutely in the last. The first 
part of the major, containing the condition, is 
called the antecedent ; and the last, which con- 
tains the conclusion, the consequent. If the 
antecedent be admitted in the minor premise, 
the consequent must be admiitod in the conclu- 
sion ; for the condition, stated in the antece- 
dent, must always be such as necessarily to 
require the truth of the consequent. By the 
same necessity it will follow, that, if the conse- 



IRREGULAR SYLLOGISMS. 135 

quent be contradicted in the minor, the ante- 
cedent must be contradicted in the conclusion. 
Thus, 

If death be an eternal sleep, the Scriptures are not true ; 
But the Scriptures are true ; 
Therefore death is not an eternal sleep. 

179. In conditional syllogisms then there are 
two ways of reasoning, which lead to certain 
conclusions. The first is called arguing from 
the position of the antecedent to the position 
of the consequent ; and the other, arguing from 
the removal: of the consequent to the removal 
of the antecedent. These are the only modes 
of true reasoning in this sort of syllogism ; for 
we are not at liberty to adopt the contrary 
course, and argue from the admission of the 
consequent to the admission of the antecedent, 
nor from the removal of the antecedent to the 
removal of the consequent. This will be man- 
ifest in the following example : 

If W. were a general, he would have power ; 
But W. is not a general ; 
Therefore he has not power. 

If W. be a general, he must be obeyed; 
But W. must be obeyed ; 
Therefore he is a general. 



136 IRREGULAR SYLLOGISMS. 

The falsehood of the consequent will not fol- 
low from the falsehood of the antecedent, nor 
the truth of the antecedent from the truth of 
the consequent. The one may be true, and 
the other may be false, for different reasons 
from those, which are assigned. 

180. A disjunctive syllogism is one, whose 
major premise is disjunctive. Thus, 

The world is either self-existent, or the work of some 

finite, or of some infinite Being ; 
But it is not self-existent, nor the work of any finite 

being ; 
Therefore it is the work of an infinite Being. 

The business of the major proposition of this 
syllogism appears to be to enumerate several 
predicates, of which one only can belong to the 
subject. If then the minor establishes one of 
these predicates, the conclusion must remove 
all the rest ; or if, in the minor premise, all the 
predicates but one are removed, the conclusion 
must establish that, which remains. This pro- 
cedure has been denominated arguing from the 
assertion of one to the rejection of the rest ; 
or, from the denial of one, two, or more, to the 
establishment of the remainder. But the term 
arguing is applied to it without any good 



COMPOUND SYLLOGISMS. 137 

reason, since it is nothing more than a formal 
and circuitous method of stating a fact. 



CHAPTER THIRTEENTH. 

COMPOUND SYLLOGISMS. 

181. A compound syllogism consists of more 
than three propositions^ and may he resolved 
into tivo or more syllogisms. Of these the prin- 
cipal kinds are the Epichirema^ Dilemma^ and 
Sorites. 

The Epichirema is a compound argument^ 
ofivhich the major and minor premises are sep- 
arately proved^ before the conclusion is draivn. 
Example. 

Unjust laws endanger the stability of government ; for 

they create discontent among the people ; 
Laws, which restrain the freedom of conscience, are 

unjust ; for they require people to abandon their 

dearest concerns ; 
Therefore laws, which restrain the freedom of conscience, 

endanger the stability of government. 

The major and minor premises, with their 
respective proofs, form two enthymemes, which 
may readily be reduced to regular syllogisms. 
Discard these proofs, and a regular syllogism 
will remain. 
12^ 



138 COMPOUND SYLLOGISMS* 

182. The epichirema is much used in con- 
versation, publick harangues, and oratorical 
discourses. Cicero's defence of Milo is an 
argument of this sort. His first position is, that 
it is lawful for one man to kill another^ who lies 
in ivait to kill him. This he proves from the 
laws of. nature and the customs of mankind. 
His second position is, that Clodius lay in wait 
for Miloy ivith a murderous intent ; which he 
proves by his equipage, arms, guards, and 
other circumstances. Then he infers the con- 
clusion, namely, that it was lawful for Milo to 
kill Clodius. 

1 83. The Dilemma^ is a compound argument^ 
which establishes a general conclusion^ either 
directly by proving its necessity^ or indirectly 
by showing the impossibility or absurdity of its 
contrary^ in every supposable case. Thus, 

Every magistrate must either execute the laws, or suffer 

them to be violated ; 
If he execute them, he will be hated by the vicious and 

profligate : 
If he suffer them to be violated, he vrill be hated by the 

wise and virtuous ; 
Therefore, every magistrate is exposed to hatred from his 

fellow men. 

* Aij; bisy and \anpdvu>, caph. 



COMPOUND SYLLOGISMS. 139 

The subject of the conclusion is first divided 
into two classes, namely, those magistrates, 
who do, and . those who do not execute the 
laws. The attribute, hatred^ is then affirmed 
of each class separately, and is finally predi- 
cated of the whole subject. This dilemma 
may \>e resolved into three regular syllogisms. 
The major premise Und the conclusion, taken 
together, constitute a regular enthymeme ; and 
the four intervening propositions form two 
enthymemes, hypothetically stated. 

184. Pyrrho, the ancient sceptick, asserted, 
that no one can have certain knowledge of any 
thing. One of his friends reproved him in the 
following dilemma : 

You either know what you say to be true, or you do not 

know it ; 
If you do know it to be true, that very knowledge proves 

your assertion to be false, and you do wrong to make 

it; 
If you do not know it to be true, you do wrong to assert 

it, since no one has a right to assert what he does not 

know to be true ; 
Therefore, in either case, you do wrong to assert, that no 

one can have certain knowledge of any thing. 

185. A dilemma is a form of argument 
frequently employed both in moral and math- 



140 COMPOUND SYLLOGISMS. 

ematical reasoning. The geometrician adopts 
this method, when, in order to prove the 
equality of two hnes or angles, he first assumes, 
that, if they are not equal, one must be either 
greater or less than the other ; and, having 
removed both these suppositions, he thence in- 
fers, that the proposed lines or angles are equal. 
186. In order to understand fully the prin- 
ciple of reasoning in a dilemma, it is necessary 
to consider the major premise as conditional, 
the first part of which is commonly omitted, to 
wit, the antecedent, w^hich consists of a general 
assertion, conditionally made, which it is the 
object of the dilemma to disprove. What 
usually appears as the major premise, is only 
the consequent of this member, consisting of an 
enumeration of all the suppositions, of which 
the subject will admit.^ If then all these sup- 
positions be rejected in the minor premise, the 
antecedent will of necessity be rejected in the 
conclusion. This reasoning proceeds univer- 

* By supplying the antecedent in the example first 
stated, the major premise will stand thus : 

if all magistrates be not exposed to the hatred of their fellow 
men, it is either because they execute the laws, or suffer them to be 
violated. 



COMPOUND SYLLOGI&MS. 141 

sally from the removal of the consequent to 
the removal of the antecedent. 

187. A dilemma may be defective in two 
ways ; first, when the conditions are not ac- 
curately stated in the major premise ; secondly, 
when the argument may be retorted with equal 
force on him, who offers it. A remarkable 
instance of the retort of a dilemma happened 
in the singular controversy between Protagoras 
and Euathlus. The former engaged to teach 
the latter the art of pleading for a stipulated 
reward, one moiety of which was to be paid 
in hand, and the other when the pupil gained 
his first cause at court. After a short time 
Protagoras sued Euathlus for the remaining 
moiety of the money, and made use of this 
dilemma : 

The case must be decided either in my favour or in 

yours ; 
If it is decided in my favour, the sum will be due to me 

according to the sentence of the judge ; 
If it is decided in your favour, it will be due to me by 

virtue of our contract ; 
Therefore, whether I gain or lose the cause, I shall obtain 

the reward. 

Euathlus thus retorted the dilemma. 



142 ^ COMPOUND SYLLOGISMS. 

t shall either gain the cause, or lose it ; 

If I gain the cause, nothing will be due to you according 

to the sentence of the judge ; 
If I lose the cause, nothing will be due to you according 

to our contract ; 
Therefore in neither case shall I pay you the reward. 

Sometimes the consequent of the major consists 
of more than two parts, and then the syllogism 
is called a trilemma^ tesseralemma^ and so on. 

188. The Sorites^ is an irregular^ compound 
argument^ consisting of a series of propositions^ 
arranged in such a raanner^ that the predicate 
of each preceding proposition, forms the subject 
of that which follows ; and the concluding prop- 
osition unites its predicate to the subject of the 
first. Thus, 

Avaricious men have many desires ; 

They, who have many desires, are in want of many things ; 
They, who are in want of many things, are unhappy ; 
Therefore avaricious men are unhappy. 

This example contains the substance of two 
syllogisms, which may be thus stated in regu- 
lar form : 

I. 

Those, who have many desires, are in want of many things ; 

Avaricious men have many desires ; 

Therefore avaricious men are in want of many things. 

* Swpoj; congeries, acermis. 



COMPOUND SYLLOGISMS. 143 

11. 

Those, who want many things, are unhappy ; 
Avaricious men want many things ; 
Therefore avaricious men are unhappy. 

189. Every sorites may be resolved into as 
many syllogisms as it contains middle terms ; 
or as it has propositions intervening between 
the first and the last. The second proposition 
of the sorites forms the major premise of the 
first syllogism ; the third, the major of the 
second, and so on. The folloY\^ing example 
may be reduced to four syllogisms. 

The mind is a thinking substance ; 

A thinking substance is a spirit ; 

A spirit has no composition of parts ; 

That, which has no composition of parts, is indissoluble ; 

That, which is indissoluble, is immortal ; 

Therefore the mind is immortal. 

190. A sorites may be formed of hypotheti- 
cal enthymemes, any number of which may be 
so joined in a series, that the consequent of 
each shall become the antecedent of the next 
following; in which case, by establishing the 
antecedent of the first, we establish the conse- 
quent of the last ; or, by removing the conse- 
quent of the last, we remove the antecedent of 



144 SOPHISMS. 

the first. This is manifest in the following 
example : 

If men are to be punished in another world, God must be 

the punisher ; 
If God be the punisher, the punishment must be just ; 
If the punishment be just, the punished must be guilty ; 
If the punished be guilty, they could have done otherwise ; 
If they could have done otherwise, they were free agents ; 
Therefore, if men are liable to punishment in another 

world, they must be free.* 



CHAPTER FOURTEENTH. 

SOPHISMS. 

191. A knowledge of the different kinds of 
reasoning, with their respective laws and 
principles, is of important use in enabling us 
to detect the sophistry and false reasoning 
employed in the support of error. But the 
rules of logick are of little service, till habit 
has rendered them familiar. By frequently 
examining the judgments and conclusions 
which we have formed, and comparmg them 
with those rules of procedure, which lead to 
certain results, we insensibly acquire the habit 

* Common systems of Logick. Locke, Essay on the Understand- 
mg, b. iv. ch. 17. 



SOPHISMS. 145 

of conducting our intellectual processes with 
accuracy, and also a facility in detecting the 
false deductions of others, 

192. Arguments^ which contain a latent 
fallacy under the general appearance of cor- 
rectness^ are denominated sophisms. They 
have been distinguished into various kinds^ 

^ from v^hich the following are selected, as those 
which are practised with the greatest frequency 
and success. 

193. First. Ignoratio Elenchi, a misappre- 
hension of the question. This sophism is com- 
mitted when the arguments employed are of 
a nature to establish some other point, foreign 
to the question in debate ; as if a person should 
attempt to prove, that Alfred the Great was a 
scholar, by affirming only, that he founded the 
University of Oxford ; or, that Peter the Her- 
mit was not a Christian, by proving that he 
was an ignorant fanatick. Neither of these 
facts has any necessary connexion with the 
question to be proved for a mar, may be 
a patron of science, without being learned 
himself ; and an ignorant fanatick may be a 
believer in Christianity. 

194. Disputants are frequently guilty of this 

13 



146 SOPHISMS. 

fallacy, when, in the heat of controversy, they 
wander insensibly from the precise subject of 
discussion. It is also sometimes committed 
by design ; as when a disputant, finding his 
adversary too powerful, or his position un- 
tenable, endeavours to gain an a^dvantage by 
altering the question. The only effectual 
security against this species of sophistry is, to 
have the subject accurately defined, and to 
keep it steadily in view. 

195. Secondly. Petitio Frincipii^ a begging 
of the question. This consists in offering, as 
proof of a proposition, the substance of that 
proposition in other words. Thus a person 
attempts to prove, that God is eternal, by as- 
serting that his existence is without beginning 
and without end. The proof and the question 
to be proved are substantially the same. This 
fallacy is often practised in familiar conversa 
tion. Thus a person asks, why opium induces 
sleep ? He is answered, because it possesses 
a soporifick quality ; which is equivalent to 
saying, that it induces sleep because it indu- 
ces sleep. So we are told, that the grass 
grows by means of its vegetative power ; and 



SOPHISMS. 147 

that bodies tend to the centre, by reason of 
their gravitation. 

196. Thirdly. Arguing in a circle. This is 
a kind of sophistry nearly related to the pre- 
ceding ; and consists in making two proposi- 
tions reciprocally prove each other. Thus, the 
Papists prove the truth of the Scriptures, by 
the infallible testimony of the church ; and 
then establish the infallibility of the church, 
by the authority of the Scriptures. The Ne- 
cessarians practise this sophistry, when they 
bring their hypothesis to prove a fact, and 
then allege the fact, as proof of their hypoth- 
esis. They first assume, gratuitously^ that the 
mind acts mechanically, like the body ; and 
that it never can act, unless the motive, which 
causes the action, be greater than any other, 
thee existing in the mind. Any particular vo- 
lition is then declared to be necessary^ because 
the motive, which produced it, was the strong 
est then in the mind. But when asked for the 
proof, that this motive was the strongest, they 
simply refer us to the volition, which othenvise 
could not have taken place. That is, the 
volition was necessary^ because it was produced 
by the strongest motive ; and the motive must 



148 SOPHISMS. 

have been the strongest^ because the volition 
was produced. 

197. Fourthly. Non causa pro causa; or 
the assignation of a false cause. From an un- 
willingness to be thought ignorant, people often 
impose on themselves, and on the credulity of 
their fellow men, by assigning, as the cause of 
an event, something, that has no perceivable 
connexion with it. Among illiterate people, 
rare occurrences are sometimes thought to have 
a connexion, barely on account of their proxim- 
ity in time or place. Thus, should the ap- 
pearance of a comet be followed by a famine, 
pestilence, or any other grievous calamity, 
many people v/ould consider the comet as the 
cause of that calamity. So, if a person have 
committed any flagrant crime, and shortly 
after meet with some distressing evil, the for- 
mer is readily believed to have been the cause 
of the latter. This sophism is practised by all 
those impostors, who make pretensions to 
supernatural skill in interpreting enigmatical 
circumstances, and in presaging future events, 
from dreams and other omens ; by which means 
they flatter the superstition and credulity of 
mankind. 



METHOD. 149 

198. Fifthly. Another species of sophistry 
is called fallacia accidentis. This consists in 
pronouncing concerning the general nature or 
properties of a thing, from some accidental 
circumstances. As when certain amusements 
are condemned, as universally unlawful, because 
they are occasionally carried to excess. So 
religion has been denounced, as an evil to 
mankind, because it has sometimes been as- 
sumed as a cover for crimes. If a medicine 
have operated unfavourably, weak persons are 
ready to reject it universally ; or, if its good 
effects have been extraordinary, they are ready 
to adopt it in all cases whatsoever. This is 
the great cause of error, the substitution of 
local, partial, temporary connexions, for uni- 
versal and unchangeable. The great remedy 
of error is the extensive observation and com- 
parison of particulars, or laborious induction ; 
and this is the true logick. 



CHAPTER FIFTEENTH. 

DISPOSITION OR METHOD. 

199. Method, in logick, is a proper classiS- 
cation and arrangement of our thoughts on any 
13* 



150 METHOD- 

subject, either to facilitate the discovery of new 
truths, or to assist us m communicating to oth- 
ers truths aheady known ; or, lastly, to enable 
us to preserve for future use the knowledge, 
Vv hich we have acquired. The disposition best 
adapted to the investigation of truth is the 
analytick method ; which is therefore denomi- 
nated the method of invention ; and that which 
is best suited to the communication of knowl- 
edge, is the synthetick method^ which for this 
reason has been called the method of instruc- 
tion. In both of these methods, ideas are 
arranged in such order, as to exhibit their 
mutual connexions and relations, 

200. Analysis^' signifies an operation^ by 
•which some process of art is retraced^ or some 
compound subject is reduced to its elementary 
parts. Synthesisf implies the act of collecting 
or putting together. By the first we begin 
with the whole, and proceed by successive 
steps to the parts, of which it is composed ; by 
the last we begin with the parts, or the most 
general principles, and proceed by combining 
them in due order to make up the whole. 

* *AvaXv«; resdvo. t "ZwridTjuh ccnjungo, compono, , 



METHOD- 151 

201. Analysis and synthesis are terms of 
frequent use in many sciences, but they have 
not invariably the same signification annexed to 
them. They always, however, denote opposite 
processes, one beginning where the other ter- 
minates ; and they reciprocally explain each 
other. They may be sometimes both employ- 
ed with equal advantage in explaining the 
same thing. Thus, the mechanism of a com- 
plicated machine may be shown by either 
method. We may do it analytically, by taking 
the machine, in its entire state, and separating 
its parts in the reverse order of their com- 
bination, carefully explaining eacli pai ; is wo 
proceed, till we arrive at that, with which the 
mechanical construction commenced. Or we 
may adopt the synthetick method, and, begin- 
ning with the parts, in a state of separation, 
place them successively in their former order, 
till the combination is restored. 

202. Most of the improvements in the dif- 
ferent sciences and arts have been made by 
analysis. It is by this method, that things have 
been ranked into classes. A species is formed 
by analyzing individuals ; and a genus by an- 
alyzing species. We practise the same meth- 



152 METHOD, 

od in learning to read the language of our 
country. We first acquaint ourselves with the 
letters of the alphabet. We next trace out 
their powers, by observing in what manner they 
are sounded, as they are variously combined in 
syllables and words. In this way we at length 
acquire some general rules, by which we can 
readily give to each letter its appropriate 
sound, in any new combination. By the same 
method we learn a foreign language, and uni- 
versal grammar ; also the philosophy of mind, 
anatomy, chemistry, botany, and other branches 
of natural knowledge. 

203. The synthetick method is not adapted 
to the investigation of new truths, and is rarely 
employed for that purpose. It is a process of 
composition ; and consists in putting together 
a number of things in a particular manner, so 
as to accomplish some end proposed. But in 
order to do this, it is necessary for a person 
previously to possess the knowledge, which it 
is the object of the operation to evince. With- 
out this knowledge, he would have nothing to 
guide him in the selection or arrangement of the 
parts ; and would be in the condition of a man, 
who should undertake to make some very com- 



METHOD. 153 

pound medicine, without knowing the ingredi- 
ents, of which it is composed. By successively 
mixing substances of different kinds, and in 
various proportions, directed only by casual 
circumstances or mere conjecture, it is possi- 
ble for him ultimately to succeed ; but this 
would not be likely to happen, till after 
much waste of time and many unsuccessful 
efforts. 

204. The superiority of the analytick over 
the synthetick method, in the investigation of 
new truths, is very forcibly shown by Mr. 
Stewart in the following example : " Suppose 
" a knot, of a very artificial construction, to be 
^' put into my hands, as an exercise for my 
" ingenuity ; and that I was required to inves- 
" tigate a rule, which others, as well as myself, 
" might be able to follow in practice, for mak- 
^'ing knots of the same sort. If I were to 
" proceed in this attempt according to the 
" spirit of a geometrical synthesis, I should 
" have to try, one after another, all the vari- 
''ous experiments, which my fancy could de- 
" vise, till I had at last hit upon the particular 
" knot I was anxious to tie. Such a process, 
" however, would evidently be so completely 



154 METHOD, 

" tentative, and its final success would after all 
*' be so extremely doubtful, that common sense 
" could not fail to suggest immediately the idea 
" of tracing the knot through all the various 
'' complications of its progress, by cautiously 
" undoing or unknitting each successive turn 
" of the thread, in a retrograde order, from the 
" last to the first. After gaining this first step, 
" were all the former complications restored 
'' again, by an inverse repetition of the same 
'' operations, which I had performed in uiidoing 
" them, an infallible rule would be obtained for 
'' solving the problem originally proposed.""^ 

205. Though knowledge is chiefly acquired 
by the analytick method, it is most convenient- 
ly conveyed to others by the synthetick. The 
teacher uses one method, while the pupil 
practises the other. The synthetick method 
is the most plain, concise, and regular. It 
coincides with the order, in which the useful 
arts are practised, and most of the business 
of life is transacted. It begins with the most 
general and obvious principles, and leads the 
mmd directly from known truths to those 
which are unknown. Instruction in every 

• Elem of the Phil, of the Mind, vol. ii. oh. 4. sect. 3. 



METHOD. 156 

science is given synthetically. It consists in 
prescribing rules more or less general ; and 
these rules are nothing more than the results 
of analytical processes previously performed. 

206. The other purpose of method is to 
secure to the mind a command over the knowl- 
edge it has acquired. Memory includes the 
power of treasuring up and preserving ideas ; 
and also that of recalling them, when we have 
occasions for applying them to use. The lat- 
ter power is usually termed recollection. In 
respect of both these faculties, the burden of 
memory is diminished by arranging the sub- 
jects of our knowledge under distinct heads, 
and charging the memory with some leading 
objects, only, in each class. But the same form 
of arrangement will not equally contribute to 
render the memory retentive and ready. ^ For 
this reason, no plan can be prescribed, which 
will be equally beneficial to all. 

207. People, engaged in the active business 
of life, are under the necessity of carrying in 
their minds a multitude of particulars, which 
are of no further use, than to assist them in the 
daily business of their calling. To such per- 

* Stewart, Elem. vol. i. ch. G. sect. 2. 



156 METHOD. 

sons a prompt recollection is of the highest im- 
portance, as it contributes to the despatch of 
business. They will therefore seek an ar- 
rangement, with reference to this object : and 
the surest method of effecting it is an arbitrary 
one, suggested by the circumstances of their 
situation, all which are of a local and tempo- 
rary nature. While they continue their ha- 
bitual pursuits, their thoughts will be succes- 
sively called up by the objects oflfered to their 
senses ; but on changing their situation, so as 
to lose their familiarity with those objects, the 
ideas, which were associated with them, must 
in a short time be irretrievably lost. 

208. A different method of arrangement is 
necessary, to give the mind a durable posses- 
sion of the acquisitions it has made. The 
only arrangement, capable of effecting this 
purpose, is that, which refers the truths, we are 
solicitous to preserve, to the general principles, 
with which they are connected. By having 
our ideas distributed according to this method, 
reason can lend its aid to the powers of memo- 
ry, by tracing the natural relations and con- 
nexions of things, and thus deducing one truth 
from another. Some sort of arrangement or 



RULES OF CONTROVERSY. 157 

Other is indispensable to persons of every con- 
dition ; otherwise but a small proportion of 
the thoughts, which pass through the mind, 
could by any effort be recalled. 



CHAPTER SIXTEENTH. 

RULES OF CONTROVERSY. 

209. From the limited extent of human 
knowledge, and the different points of view, in 
which the same subjects may be contemplated 
by different minds, it follows of necessity, that 
a diversity of opinions must be entertained on 
many subjects of speculation. In whatever 
manner people are first led to form their opin- 
ions, they are usually disposed to defend them 
afterwards with zeal and pertinacity. Hence 
arise controversies and disputes, which are 
oftentimes conducted with such intemperate 
and misguided zeal, as to inflame animosities, 
by which the comfort and harmony of society 
are impaired. 

210. These are the worst fruits of contro- 
versy. They are, however, merely incidental 
effects ; and are counterbalanced by others of 
an opposite character, and of high importance 

14 



158 RULES OF COINTROYERSY. 

to the interests of truth and virtue. The 
advantages of controversy consist in having 
questions of difficulty and moment settled in a 
satisfactory manner. The principles of gov- 
ernment and law have been immovably fixed 
by the debates, which have passed in deliber- 
ative assemblies and in courts of justice. 

211. All questions, not susceptible of rigor- 
ous demonstration, can be correctly settled 
only by a full and impartial comparison of the 
reasons on both sides. This is seldom done, 
with sufficient exactness, by the solitary inves- 
tigation of an individual. Men rarely enter 
on the examination of a question wholly free 
from the bias of a previous opinion respecting 
it, which makes them more solicitous to find 
arguments for one side than for the other. 
It is only when the talents of different persons 
are enlisted, and opposite opinions are contend- 
ed for, that questions are traced in all their 
bearings, and the grounds of an equitable 
decision are fully exhibited. 

212. The importance of controversy may be 
mferred from the use, which has been made of 
it, in every period of the world. It has been 
adopted, as the principal mode of transacting 



RULES OF CONTROVERSY. 159 

business, in the halls of legislation and in courts 
of justice, where questions of the deepest con- 
cern to individuals and communities are decid- 
ed. The minds of youth have been trained 
to it in seminaries of education, where the 
practise of disputation, in Various forms, has 
been preserved, as a salutary disciphne of the 
mental powers. 

213. As controversy, especially when carried 
on from motives of victory or reputation, is 
liable to be productive of evil rather than of 
good, it is incumbent on all, who engage in it, 
from whatever motives, to observe rigorously 
those laws and principles, by which the former 
may be avoided and the latter secured. The 
following rules, sometimes called canons of 
controversy, have been highly approved by 
w Titers of learning and discernment.* 

214. Rule 1st. The terms^ in ivhich the ques- 
tion in debate is expressed^ and the precise point 
at issue^ should he so clearly defined^ that 
there could he no misunderstanding respecting 
them. If this be not done, the dispute is liable 
to be, in a great degree, verbal. Arguments 

* These rules are taken, with slight alterations, from the lectures 
of Dr. Hey, Norrisian Professor in the University of Cambridge. 
They may also be found in Kirwan's Logick, vol. ii. 



160 RULES OF CONTROVERSY. 

will be misapplied, and the controversy pro- 
tracted, because the parties engaged in it have 
different apprehensions of the question. 

215. Rule 2d. The parties should mutually 
consider each other^ as standing on a footing of 
equality in respect to the subject in debate. 
Each should 7 egard the other as possessiiig 
equal talents knoivledge^ and desire for truthj 
with himself ; and that it is possible^ therefore^ 
that he may be in the wrongs and his adversary 
in the right. In the heat of controversy, men 
are apt to forget the numberless sources of 
error, which exist in every controverted sub- 
ject, especially of theology and metaphysicks. 
Hence arise presumption, confidence, and 
arrogant language ; all which obstruct the 
discovery of truth. 

216. Rule 3d. All expressions^ ivhich are 
unmeaning^ or voithout effect in regard to the 
subject in debatCj should be strictly avoided. 
All expressions may be considered as unmean- 
ing, which contribute nothing to the proof of 
the question ; such as desultory remarks and 
declamatory expressions. To these may be 
added all technical, ambiguous, and equivocal 
expressions. These have a tendency to dazzle 



RULES OF CONTROVERSY. 161 

and bewilder the mind, and to hinder its clear 
perception of the truth. 

217. Rule 4th. Personal reflections on an 
adversary should in no instance be indulged. 
Whatever be his private character, his foibles 
are not to be named nor alluded to in a con- 
troversy. Personal reflections are not only 
destitute of effect, in respect to the question 
in discussion, but they are productive of real 
evil. They obstruct mental improvement, and 
are prejudicial to publick morals. They mdi- 
cate in him, v^ho uses them, a mind hostile to 
the truth ; for they prevent even solid argu- 
ments from receiving the attention, to which 
they are justly entitled. 

218. Rule 5th. No one has a right to accuse 
his adversary of indirect motives. Arguments 
are to be answered, whether he, who offers 
them, be sincere or not, especially as his want 
of sincerity, if real, could not be ascertained. 
To inquire into his motives, then, is useless. 
To ascribe indirect ones to him is worse than 
useless ; it is hurtful. 

219. Rule 6th. The consequences of any doc-^ 
trine are not to he charged on him^ loho maintains 
it, unless he expressly avows them. If an absurd 

14^ 



162 RULES OF INTERPRETATION. 

consequence be fairly deducible from any doc- 
trine, it is rightly concluded that the doctrine 
itself is false ; but it is not rightly concluded, 
that he, who advances it, supports the absurd 
consequence. The charitable presumption, in 
such a case, would be, that he had never made 
the deduction ; and that, if he had made it, he 
would have abandoned the original doctrine. 

220. Rule 7th. As truth, and not victory, 
is the professed object of controversy, ivhatever 
proofs may be advanced, on either side, should 
be examined idth fairness and candour; and any 
atteinpt to ensnare an adversary by the arts of 
sophistry, or to lessen the force of his reasonings 
by ivit, cavilling, or ridicule, is a violatio7i of 
the rides of honourable controversy. 



CHAPTER SEVENTEENTH. 

RULES OF INTERPRETATION. 

221. To ascertain the true meaning of a 
written document is often difficult and embar- 
rassing, even when it is of recent date and in 
our own language ; but the difficulty is gi'eatly 
enhanced, when the writing is in a foreign 
language, or has descended from ancient times. 



RULES OF INTERPRETATION. 163 

222. The circumstances, which aggravate 
the labour of the interpreter, are numerous, and 
of various kinds. No branch of knowledge is 
entirely exempt from them ; but they exist in 
the greatest degree in those sciences, which 
involve our most important interests, both 
sacred and civil. For this reason, principles 
and rules of interpretation have been carefully 
formed for developing the true meaning of the 
sacred Scriptures and of legal instruments. 

223. The design of interpretation is to 
ascertain the real intention of the writer ; to 
develope the true meaning of his words, where 
they are obscure or ambiguous ; and to deter- 
mine what was his design, where his words do 
it but imperfectly. The following rules are of 
a general character, and may be employed 
with equal advantage, in explaining writings 
of every kind : 

224. Rule 1st. The interpreter of a written 
document must have a thorough knowledge of 
the language, in which it is written. 

225. Rule 2d. He must possess an intimate 
acquaintance with the subject of the writing. 
Many words have different significations in 
different sciences and arts ; and the particular 



164 RULES OF INTERPRETATION. 

meaning they were intended to convey, in any 
instance, must be agreeable to the nature of 
the subject, on which they were employed. 

226. Rule 3d. The true interpretation of a 
writing often requires a knowledge of the 
character of its author. His peculiar bent of 
mind, his temperament, his vocation, and 
especially his political or religious tenets, may 
have had an influence, for which some allow- 
ance should be made. 

227. Rule 4th. If the writing to be interpret- 
ed be of ancient date, the interpreter should 
ascertain the genuineness of his text ; whether 
it has descended to him as it came from the 
author, without any corruptions or interpola- 
tions from other hands. 

228. Rule 5th. The interpreter should also 
be well acquainted with the history of the coun- 
try and of the period, in which his author wrote. 
Words have different meanings indifferent ages; 
and writers are insensibly influenced by the 
existing fashions, and other circumstances of 
a local and temporary nature. 

229. Rule 6th. The mind of the interpreter 
should be wholly free from all antecedent bias 
in favour of any system, doctrine, or creed, 



RULES OF INTERPRETATION. 165 

which might influence his judgment, in the 
interpretation he is about to make. 

230. Rule 7th. In making the interpretation 
of a document, the subject and predicate of 
each proposition should be carefully distin- 
guished , the various sentences and clauses 
should be construed in reference to each 
other ; and the resulting sense of all the parts 
should be connected and consistent. 

231. Rule 8th. Words, which admit of 
different senses, should be taken in their most 
common and obvious meaning, unless such a 
construction lead to absurd consequences, or 
be inconsistent with the known intention of 
the writer. 

232. Rule 9th. When any word or expres- 
sion is ambiguous, and may, consistently with 
common use, be taken in different senses, it 
must be taken in that sense, which is agreeable 
to the subject, of which the writer was treat- 
ing. 

233. Rule 10th. Doubtful words and phrases 
must always be construed in such a sense as 
will make them produce some eflTect ; and not 
in such a sense as will render them v^hoUy 
nugatory. 



166 RULES OF INTERPRETATION. 

234. Rule 11th. Violations of the rules of 
grammar do not vitiate a writing, in which the 
sense is distinctly expressed. When a pas- 
sage is imperfect, or unintelligible, the inter- 
preter is at liberty to supply such words, as 
are manifestly necessary to render its sense 
complete. But he is not allowed, in a sim- 
ilar case, to expunge certain words from the 
text, in order to give an intelhgible meaning 
to those that remain. 

235. Rule 12th. When there are no special 
reasons for the contrary, words should be con- 
strued in their literal, rather than in their fig- 
urative sense ; relative words should be refer- 
red to the nearest, rather than to a remote 
antecedent ; and words, which are capable of ^ 
being understood in either, should be taken in 
their generick, rather than in their specifick 
sense. 

236. Rule 13th. However general may be 
the words, in which a covenant is expressed, it 
comprehends those things, only, on which it 
appears the parties intended to contract, and 
not those, which they had not in view. But 
when the object of the covenant is an univer- 
sality of things, it comprehends all the particu- 



RULES OF INTERPRETATION. 167 

lar things, which compose that universahty, 
even those, of which the parties had no 
knowledge. 

237. Rule 14th. Whatever is obscure or 
doubtful in a covenant should be interpreted 
by the intention of the parties. If the inten- 
tion of the parties does not appear from the 
words of the covenant, it should be inferred 
from the existing customs and usages of the 
place, in which it was made. If the words of 
.a covenant contradict the well known intention 
of the parties, this intention must be regarded 
rather than the words. ^ 

238. Rule 13th. When former interpreters 
are appealed to, in order to establish the sense 
of an ancient writing, those, cceteris paribus^ 
should be preferred, who were nearest the au- 
thor, in time or place, as his children, pupils, 
correspondents, or countrymen ; and who had, 
therefore, better advantages for knowing his 
mind, than more distant commentators. 

* Sarti, Dialect. Instit. Kirwan, Logick. Le Clerc, Ars Critica. 
Vattel, Law of Nations. Rutherforth, Lectures on GrotJus. Gilbert, 
Law of Evidence. Pothier on Obligations. Domat on the Civil Law. 



168 CONCLUDING REMARKS. 



CONCLUDING REMARKS. 



In the preceding summary, an attempt has 
been made to state and explain those rules of 
intellectual discipline, which may guide and 
improve the reasoning faculties. As the work 
is intended to be strictly elementary, general 
principles only have been given, with such plain 
examples, as might limit and illustrate their 
meaning. The following remarks are subjoin- 
ed for the use of those, who may wish to ex- 
tend their inquiries on the subject of logick, 
and the philosophy of the human mind. 

Dr. Reid's analysis of Aristotle's Logick 
contains a brief but comprehensive exposition 
of the syllogistick system. A more full ac- 
count of the categories, together with the vari- 
ous laws of syllogistick reasoning, may be 
found in the logical treatises of Burgersdicius 
and of Le Clerc. 

Of modern systems of logick, those f Watts 
and of Duncan have been most approved. A 
more recent and valuable treatise, than either 
of these, is that of Kirwan. 

It is essential to accurate reasoning to dis- 
tinguish those first principles of human knowl- 



CONCLUDING REMARKS. 169 

edge, which must be taken for granted, from 
those propositions, which require proof. On 
this subject the treatise of Father BufRer, en- 
titled First Truths, Beattie's Essay on Truth, 
and Condillac on the Origin of Knowledge, 
are valuable sources of information. 

The Novum Organum of Lord Bacon con- 
tains in a small compass those rules of induc- 
tive logick, which have been followed with the 
happiest success, both in physical researches, 
and in the philosophy of the mind. 

On tke subject of moral reasoning, important 
information may be derived from Gambler's 
Introduction to Moral Evidence, and from the 
first book of CampbelPs Philosophy of Rhet- 
orick. 

For the general direction of the mind, in its 
researches after truth, rules of a more practi- 
cal nature may be found in Locke's Conduct 
of the Understanding, and Watts on the Im- 
provement of the Mind. 

The study of those authors, who reason 
clearly and accurately, is one of the best 
methods of improving the reasoning powers. 
For this purpose, Berkeley on the Principles of 
Human Knowledge, Wollaston on the Religion 
15 



170 CONCLUDING REMARKS. 

of Nature, and Baxter on the Soul, may be 
read with great advantage. The catalogue 
might easily be extended if it were thought 
necessary. It will be concluded by referring 
the student to the metaphysical writings of 
Locke, Reid, Stewart, and Brown. They may 
be consulted with great benefit, on each of the 
subjects above mentioned ; and may be said 
to comprise in themselves a complete system 
of intellectual philosophy. 

But the student should remember, that nei- 
ther learning the best rules, nor reading the best 
models, can supersede the necessity of intent 
and continued reflection. He should dwell on 
the operations of his own mind, and mark the 
difficulties, which prevent his arriving at clear 
conclusions ; whether they arise from misap- 
prehension of the subject, from the ambiguity 
of language, from weakness in the power of 
attention, or from the biases of association. 
He will thus insensibly form a logick for 
himself, which, while it embraces the rules, 
common to all minds, will be peculiarly adapted 
to the improvement of his own. 



NOTES AND ILLUSTRATIONS. 



Note A, page 17. 

I HAVE used reflection and consciousness as synony- 
mous terms, and they are so used by eminent writers on 
pneumatology. Some, however, have considered them as 
denoting operations specifically different. Dr. Reid says, 
" reflection ought to be distinguished from consciousness, 
with which it is too often confounded, even by Mr. Locke. 
All men are conscious of the operations of their own 
minds, at all times while they are awake, but there are 
few who reflect on them, or make them the objects of 
their thought. Though the mind is conscious of its 
operations, it does not attend to them ; its attention is 
turned solely to the external objects, about which those 
operations are employed."* In another place he says, 
that " attention to things external is properly called ob- 
servation^ and attention to the subjects of our conscious- 
ness, reflection.'*^ This definition of reflection is substan- 
tially the same with that of Mr. Locke, which I have 
used. - 

The foregoing passage from Dr. Reid points out a dif- 
ference in degree, rather than in kind, between conscious- 
ness and reflection. It is true that the bulk of mankind 

* Intellectual Powers, Essay I. 



172 NOTES. 

pay very little attention to their mental operations. But, 
without some degree of attention, they would have no 
consciousness of them whatever ; and so far as they do 
attend to them, so far, according to Dr. Reid's own ac- 
count, they reflect. 

The only way, by which the phenomena of the mind 
can be investigated, is by attending to its successive 
changes and operations, as they are passing ; and this 
reflex act of attention is nothing more than an effort of 
the mind to increase or prolong the consciousness of its 
own acts. Reflection on any operation of the mind pre- 
supposes the actual existence of that operation. It may 
be examined afterwards by the assistance of memory, but 
this subsequent examination cannot be denominated re- 
flection, agreeably to the strict sense of that word. Are 
we then to believe, that reflection and consciousness 
are two distinct simultaneous eff'orts ; and each of them 
difl'erent from the operation, which the mind is carrying 
on at the same time ? This would oblige us to consider 
the mind, not as simple, but as a complication of different 
powers or agents, one of which may be employed in 
watching the operations of another, while its own acts are 
exam,ined by a third. 

Dr. Reid defines reflection, " attention to the subjects 
of our consciousness,'^^ By this expression he evidently 
supposes consciousness and the subjects of consciousness 
to be diff'erent things. But the mind can be conscious 
only of what passes within itself. Consciousness, then, 
according to him, means the notice, which the mind takes 
of its own operations. Now, as he places reflection in 
attention to the subjects of our consciousness, and il 



NOTES. 173 

appears manifest, that by the subjects of consciousness 
he means nothing else than the operations of the mind, 
it follows, even from his own statement, that these terms 
are but different names for the same thing. 

In common use there seems to be a slight difference 
in the import of these terms. By consciousness is com- 
monly understood barely the mind's notice or perception 
of its own acts and modes of existence. But reflection 
is usually employed to express some degree of voluntary 
attention to the phenomena of the mind, in order to 
ascertain the laws, by which it is governed. As the bulk 
of mankind have no curiosity for such speculations, they 
have been said rarely, if ever to reflect. 



JYote B, page 121. 

Logicians have, from the earliest period, denominated 
the predicate of the conclusion the major term^ and its 
subject, the minor. The only reason, assigned for doing 
this, is, that the predicate of a proposition has a wider 
extension than the subject. But this is not a suffi- 
cient reason for calling it the major term, since, in all our 
affirmations and negations, we are invariably governed 
by the comprehension of terms, without the slightest re- 
gard to their extension. We assert the more general of 
the less general, foj this manifest reason, that the former 
is a part of the latter. We predicate the genus of the 
species, but not the species of the genus. The predicate 
of a proposition is only an attribute of the subject ; and 
15* 



174 KOTES. 

in this light it must be viewed, in order to render the 
proposition true. When, for example, we affirm that 
saffron is j'^ellow, we refer a single property to a subject, 
in which it is known to coexist with several other prop- 
erties. In doing this, we are guided by our knowledge 
of that plant, without inquiring what other bodies there 
are in existence, which have a yellow colour. And we 
proceed in the same way, when the predicate has no 
greater extension than the subject, as when we affirm that 
iron is susceptible of magnetical attraction. 

In passing from one rank of beings to another, in the 
order of their classification, we observe that each supe- 
rior class stands in the next below it. Thus we may say 
a mastiif is a dog, a dog is an animal, and an animal is^a 
being, that has life, sense, &c. It is obvious that the first 
subject contains each of the predicates that follow. 

As, in an act of judgment, one thing is perceived to be 
contained in another, so, in syllogistick reasoning, one 
proposition is shown to be contained in another, that in 
a third, and so on. This process has been aptly illus- 
trated by a collection of boxes of different sizes, placed 
one in another. In such a nest of boxes, it would be 
natural to say of that which was placed first, and contain- 
ed all the rest, that it was the largest box, and of that, 
which was in the centre, and had no other in it, that it 
was the least box. But, in giving names to the three 
terms of a syllogism, this rule of common sense has been 
violated. The less is made to contain the greater. The 
predicate of the conclusion, which is contained in each 
of the other two, is ca led the major terra, and the sub- 



NOTES. 175 

yect of the conclusion^ which contains both the others, is 
called the minor term. 



J^ote C, jpage 122. 

This is true in that arrangement of parts, which renders 
the syllogism the most simple and the most perfect ; though 
it will not hold in all those technical forms, in which it has 
been expressed. 

It may not be deemed wholly impertinent in this place 
to give a brief description of that celebrated doctrine of 
modes and figures, in which simple syllogisms are involv- 
ed, in the ancient books of logick. By the 7node of a 
syllogism is meant the designation of the quantity and 
quality of its propositions. By figure is meant the 
situation of the middle term with respect to the major 
and minor terms. As the middle term occurs in each 
of the premises, it is susceptible of four diiferent positions 
in relation to the extremes. Hence four figures have 
been invented. In the first, the middle term is the sub- 
ject of the major proposition, and the predicate of the 
minor. In the second, it is the predicate, and in the 
third, the subject, of both the premises. In the fourth, it 
is the predicate of the major premise, and the subject of 
the minor. 

Each of the four figures has several modes, which are 
designated by the vowels A, E, I, ; characters, em- 
ployed by logicians to denote the quantity and quality 
of propositions. A, placed before a proposition, denotes 



176 NOTES. 

that it is an universal affirmative ; E denotes an universal 
negative ; I, a particular affirmative ; and 0, a particular 
negative. To assist the memory, the following couplet 
was contrived : 

Asserit A, negat E, verum generaliter ambae. 
Asserit I, negat 0, sed particulariter ambo. 

As all the possible combinations of three of these four 
letters, in three propositions, amount to sixty-four, this 
number of modes might be formed. But, of these, fifty- 
three are excluded by certain established rules, and one 
rejected, as useless ; leaving only ten, that are considered 
as legitimate. Several of these are repeated in different 
figures, so as to make, in the whole, nineteen conclusive 
modes. Each mode is furnished with an appropriate 
name, consisting of three syllables, and containing three 
of the vowels before named. The three syllables of the 
mode are placed before the propositions of the syllogism, 
in order that the vowel letter, which alone is regarded, 
may indicate the quantity and quality of the proposition, 
before w^hich it stands. 

To the first figure are given four modes ; which are 
denominated Barbara, Celarent, Darii, Ferio. The second 
figure has likewise four modes, namely, Caesare, Cames- 
tres, Festino, Baroco. The third has six modes, Darapti, 
Felapton, Disamis, Datisi, Bocardo, Ferison. The fourth 
has five modes, Bamarip, Camenes, Dimatis, Festapo, 
Fresison. 



NOTES. 177 

These barbarous words have been thus formed into hex- 
ameter verses : 

Barbara, Celarent, Darii, Ferio quoque, primae. 
Caesare, Camestres, Festino, Baroco, secundae. 
Tertia Darapti sibi vindicat atque Felapton ; 
Adjungens Disamis, Datisi, Bocardo, Ferison. 
Non Bamarip, Camenes, Dimg-tis, Festapo, Fresison. 



EXAMPLES. 
Figure First. 

Bar- Every animal has sensation ; 

Bar Every man is an animal ; 

Ra* Therefore every man has sensation. 

Ce- No opinions, hurtful to the morals of society, 

should be embraced ; 
La- Atheistical sentiments are hurtful to the morals 

of society ; 
Rent Therefore atheistical sentiments should not be 

embraced. 

Dor All good men love peace ; 

Ri- Some statesmen are good men ; 

J. Therefore some statesmen love peace. 

Fe- No man of dissolute habits is a safe companion ; 
Ri- Some men of learning are dissolute in their 

habits ; 
O. Therefore some men of learning are not safe 

companions. 



178 NOTES 



Figure Second, 

Car Every virtuous man is fit to be believed ; 

Mes- No liar is fit to be believed ; 

Tres, Therefore no liar is a virtuous man. 

Ba- Every true patriot tries to promote the publick 

good ; 
Ro' Some men in high stations do not try to promote 

the publick good ; 
Co. Therefore some men in high stations are not 

true patriots. 



Figure Third. 

Da- All good Christians will be saved ; 

Rap- All good Christians have sinned ; 

Ti. Therefore some, who have sinned, will be saved« 



Examples of the other modes may readily be formed. 



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